Chapter

Chapter 5
Section

Chapter Review on Quadratic Expressions

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Solutions
79 Videos

Use the distributive property to find the binomial product.

```
\displaystyle
(x + 5)(x + 8)
```

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0.37mins

Q1a

Use the distributive property to find the binomial product.

```
\displaystyle
(x - 1)(x -4)
```

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0.31mins

Q1b

Use the distributive property to find the binomial product.

```
\displaystyle
(x + 3y)(x -6y)
```

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0.31mins

Q1c

Use the distributive property to find the binomial product.

```
\displaystyle
(5a -6b)(2a + 9b)
```

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0.43mins

Q1d

Expand and simplify.

```
\displaystyle
-(k + 2)(k - 7)
```

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0.49mins

Q2a

Expand and simplify.

```
\displaystyle
w(w - 7v)(w- 3v)
```

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1.03mins

Q2b

Expand and simplify.

```
\displaystyle
7x(7x + 3y)(3x + 9y)
```

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1.25mins

Q2c

Expand and simplify.

```
\displaystyle
(y + 1)(y + 8)+ (y-8)(y + 1)
```

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0.42mins

Q2d

Expand and simplify.

```
\displaystyle
-4(2x -6)(4x -5)+3(11x + 7)( 11x - 4)
```

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Q2e

Write an algebraic expression to represent the area of the figure.

Expand and simplify.

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0.37mins

Q3

Draw a diagram to illustrate the product.

```
\displaystyle
(x + 4)^2
```

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0.41mins

Q4a

Draw a diagram to illustrate the product.

```
\displaystyle
(a + 2)^2
```

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0.37mins

Q4b

Expand and simplify.

**a)** ```
\displaystyle
(x + 6)^2
```

**b)**
```
\displaystyle
(k+ 8)^2
```

**c)**
```
\displaystyle
(p + 7)^2
```

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0.46mins

Q5abc

Expand and simplify.

**i)** ```
\displaystyle
(r- 2)^2
```

**ii)**
```
\displaystyle
(e- 9)^2
```

**iii)**
```
\displaystyle
(q- 20)^2
```

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0.40mins

Q5def

Expand and simplify.

```
\displaystyle
(b + 6)(b - 6)
```

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0.15mins

Q6a

Expand and simplify.

```
\displaystyle
(a - 7)(a + 7)
```

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0.13mins

Q6b

Expand and simplify.

```
\displaystyle
(y + 12)(y - 12)
```

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0.13mins

Q6c

Expand and simplify.

```
\displaystyle
(x - 15)(x + 15)
```

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0.12mins

Q6d

Expand and simplify.

```
\displaystyle
(e - 10)(e + 10)
```

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0.10mins

Q6e

Expand and simplify.

```
\displaystyle
(x + 6)(x - 6)
```

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0.11mins

Q6f

Expand and simplify.

```
\displaystyle
(y + 4x)^2
```

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0.21mins

Q7a

Expand and simplify.

```
\displaystyle
(7m - n)^2
```

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0.23mins

Q7b

Expand and simplify.

```
\displaystyle
(2c + 9d)^2
```

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0.24mins

Q7c

Expand and simplify.

```
\displaystyle
-2(5x + 7y)(5x - 7y)
```

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0.31mins

Q7d

Expand and simplify.

```
\displaystyle
(3a - 8c)(3a + 8c)
```

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0.19mins

Q7e

Expand and simplify.

```
\displaystyle
-(5x - 8y)(5x + 8y)
```

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0.21mins

Q7f

Use algebra tiles or a diagram to illustrate the factoring of each polynomial.

```
\displaystyle
x^2 + 9x
```

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0.40mins

Q8a

Use algebra tiles or a diagram to illustrate the factoring of each polynomial.

```
\displaystyle
3x^2 + x
```

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0.59mins

Q8b

Factor.

**a)** ```
\displaystyle
12y + 24z
```

**b)** ```
\displaystyle
11xy - 9xz
```

**c)** ```
\displaystyle
c^2 + 3c
```

**d)** ```
\displaystyle
4k - 8k^3
```

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0.53mins

Q9

Factor by grouping.

```
\displaystyle
4m^2 + 12m + 3m + 9
```

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0.24mins

Q10a

Factor by grouping.

```
\displaystyle
9k^2 - 6k + 6k -4
```

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0.26mins

Q10b

Factor by grouping.

```
\displaystyle
8x^2 + 16x - 5x -10
```

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0.31mins

Q10c

Factor by grouping.

```
\displaystyle
16x^2 - 12xy - 12xy + 9y^2
```

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0.44mins

Q10d

Factor by grouping.

```
\displaystyle
8m^2 - 16m + 4
```

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0.30mins

Q11a

Factor by grouping.

```
\displaystyle
18c^3 + 24c^2 - 8c + 6
```

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1.10mins

Q11b

Factor by grouping.

```
\displaystyle
15m^2 - 22mn + 66mn^2
```

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0.24mins

Q11c

Factor by grouping.

```
\displaystyle
ax^2z - az^2 + axz
```

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0.16mins

Q11d

A rectangle has area given by the expression `10x^2 + 5x`

. The length and width can be
found by factoring the expression. Find all possible expressions for the length and width.

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0.57mins

Q12

Illustrate the factoring of each trinomial using algebra tiles or a diagram.

```
\displaystyle
x^2 + 9x + 14
```

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1.44mins

Q13a

Illustrate the factoring of each trinomial using algebra tiles or a diagram.

```
\displaystyle
x^2 + 11x + 18
```

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1.54mins

Q13b

Illustrate the factoring of each trinomial using algebra tiles or a diagram.

```
\displaystyle
x^2 + 4x + 4
```

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0.46mins

Q13c

Factor.

```
\displaystyle
c^2 - 17c + 72
```

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0.40mins

Q14a

Factor.

```
\displaystyle
x^2 - 8x + 15
```

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0.13mins

Q14b

Factor.

```
\displaystyle
z^2- 14z + 33
```

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0.14mins

Q14c

Factor.

```
\displaystyle
x^2 + 3x - 10
```

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0.19mins

Q14d

Factor.

```
\displaystyle
x^2 + 8x -9
```

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0.13mins

Q14e

Factor.

```
\displaystyle
x^2 -2x -8
```

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0.16mins

Q14f

A parabola has equation `y = x^2 -3x - 18`

.

a) Factor the right side of the equation.

b) Identify the x-intercepts of the parabola.

c) Find the equation of the axis of symmetry

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2.54mins

Q15

Factor.

```
\displaystyle
2x^2 + 7x + 6
```

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0.23mins

Q16a

Factor.

```
\displaystyle
6y^2 + 29y + 9
```

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0.52mins

Q16b

Factor.

```
\displaystyle
6a^2 - 23a + 15
```

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0.25mins

Q16c

Factor.

```
\displaystyle
4b^2 - 5b + 1
```

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0.18mins

Q16d

Factor.

```
\displaystyle
12m^2 + 20m - 8
```

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0.32mins

Q16e

Factor.

```
\displaystyle
14k^2 -31k - 10
```

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0.32mins

Q16f

Factor.

```
\displaystyle
8x^2 + 2xy - 15y^2
```

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0.41mins

Q17a

Factor.

```
\displaystyle
5c^2 - 4cd+ 9d^2
```

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0.28mins

Q17b

Factor.

```
\displaystyle
12m^2 + 13mn + 3n^2
```

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0.30mins

Q17c

Factor.

```
\displaystyle
2w^2 - 9wx - 8x^2
```

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0.28mins

Q17d

Factor.

```
\displaystyle
24x^2 + 6xy - 9y^2
```

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0.36mins

Q17e

Factor.

```
\displaystyle
9g^2 + 4g - 10
```

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0.36mins

Q17f

A rectangle has area defined by `8x^2 + 2x - 15`

.

a) Factor to find algebraic expressions for the length and width of the rectangle.

b) If `x`

represents 12 cm, determine the perimeter and the area of the rectangle.

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3.30mins

Q18

Factor.

```
\displaystyle
x^2 - 49
```

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0.18mins

Q19a

Factor.

```
\displaystyle
y^2 - 121
```

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0.11mins

Q19b

Factor.

```
\displaystyle
4k^2 - 9
```

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0.18mins

Q19c

Factor.

```
\displaystyle
16 - 144a^2
```

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0.42mins

Q19d

Factor.

```
\displaystyle
9w^2 -25x^2
```

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0.26mins

Q19e

Factor.

```
\displaystyle
1 - 81p^2
```

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0.21mins

Q19f

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
x^2 + 14x + 49
```

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0.32mins

Q20a

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
k^2 + 8k + 16
```

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0.19mins

Q20b

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
y^2 - 10y + 25
```

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0.21mins

Q20c

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
25y^2 -70y + 49
```

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0.27mins

Q20d

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
36c^2 - 108c + 81
```

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0.25mins

Q20e

Verify that the trinomial is a perfect square. Then, factor.

```
\displaystyle
121 +176y + 64y^2
```

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0.21mins

Q20f

Determine all values of `k`

so that each trinomial is a perfect square.

`25y2 + ky + 144`

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0.29mins

Q21a

Determine all values of `k`

so that each trinomial is a perfect square.

`9x^2 - 42x + k`

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0.41mins

Q21b

Factor, if possible.

```
\displaystyle
9w^2x^2 - 24wxyz + 16y^2z^2
```

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0.31mins

Q22a

Factor, if possible.

```
\displaystyle
625 - (y -5)^2
```

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1.09mins

Q22b

Factor, if possible.

```
\displaystyle
144a^4 - 499b^4
```

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1.53mins

Q22c

Factor, if possible.

```
\displaystyle
25x^2 + 30x + 4
```

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0.20mins

Q22d