Chapter Review on Quadratic Expressions
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