Chapter
Chapter 5
Section
Solutions 79 Videos

Use the distributive property to find the binomial product.

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

0.37mins
Q1a

Use the distributive property to find the binomial product.

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

0.31mins
Q1b

Use the distributive property to find the binomial product.

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

0.31mins
Q1c

Use the distributive property to find the binomial product.

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

0.43mins
Q1d

Expand and simplify.

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

0.49mins
Q2a

Expand and simplify.

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

1.03mins
Q2b

Expand and simplify.

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

1.25mins
Q2c

Expand and simplify.

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

0.42mins
Q2d

Expand and simplify.

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

Q2e

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

Expand and simplify.

0.37mins
Q3

Draw a diagram to illustrate the product.

 \displaystyle (x + 4)^2 

0.41mins
Q4a

Draw a diagram to illustrate the product.

 \displaystyle (a + 2)^2 

0.37mins
Q4b

Expand and simplify.

a)  \displaystyle (x + 6)^2 

b)  \displaystyle (k+ 8)^2 

c)  \displaystyle (p + 7)^2 

0.46mins
Q5abc

Expand and simplify.

i)  \displaystyle (r- 2)^2 

ii)  \displaystyle (e- 9)^2 

iii)  \displaystyle (q- 20)^2 

0.40mins
Q5def

Expand and simplify.

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

0.15mins
Q6a

Expand and simplify.

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

0.13mins
Q6b

Expand and simplify.

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

0.13mins
Q6c

Expand and simplify.

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

0.12mins
Q6d

Expand and simplify.

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

0.10mins
Q6e

Expand and simplify.

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

0.11mins
Q6f

Expand and simplify.

 \displaystyle (y + 4x)^2 

0.21mins
Q7a

Expand and simplify.

 \displaystyle (7m - n)^2 

0.23mins
Q7b

Expand and simplify.

 \displaystyle (2c + 9d)^2 

0.24mins
Q7c

Expand and simplify.

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

0.31mins
Q7d

Expand and simplify.

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

0.19mins
Q7e

Expand and simplify.

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

0.21mins
Q7f

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

 \displaystyle x^2 + 9x 

0.40mins
Q8a

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

 \displaystyle 3x^2 + x 

0.59mins
Q8b

Factor.

a)  \displaystyle 12y + 24z 

b)  \displaystyle 11xy - 9xz 

c)  \displaystyle c^2 + 3c 

d)  \displaystyle 4k - 8k^3 

0.53mins
Q9

Factor by grouping.

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

0.24mins
Q10a

Factor by grouping.

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

0.26mins
Q10b

Factor by grouping.

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

0.31mins
Q10c

Factor by grouping.

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

0.44mins
Q10d

Factor by grouping.

 \displaystyle 8m^2 - 16m + 4 

0.30mins
Q11a

Factor by grouping.

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

1.10mins
Q11b

Factor by grouping.

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

0.24mins
Q11c

Factor by grouping.

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

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.

0.57mins
Q12

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

 \displaystyle x^2 + 9x + 14 

1.44mins
Q13a

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

 \displaystyle x^2 + 11x + 18 

1.54mins
Q13b

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

 \displaystyle x^2 + 4x + 4 

0.46mins
Q13c

Factor.

 \displaystyle c^2 - 17c + 72 

0.40mins
Q14a

Factor.

 \displaystyle x^2 - 8x + 15 

0.13mins
Q14b

Factor.

 \displaystyle z^2- 14z + 33 

0.14mins
Q14c

Factor.

 \displaystyle x^2 + 3x - 10 

0.19mins
Q14d

Factor.

 \displaystyle x^2 + 8x -9 

0.13mins
Q14e

Factor.

 \displaystyle x^2 -2x -8 

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

2.54mins
Q15

Factor.

 \displaystyle 2x^2 + 7x + 6 

0.23mins
Q16a

Factor.

 \displaystyle 6y^2 + 29y + 9 

0.52mins
Q16b

Factor.

 \displaystyle 6a^2 - 23a + 15 

0.25mins
Q16c

Factor.

 \displaystyle 4b^2 - 5b + 1 

0.18mins
Q16d

Factor.

 \displaystyle 12m^2 + 20m - 8 

0.32mins
Q16e

Factor.

 \displaystyle 14k^2 -31k - 10 

0.32mins
Q16f

Factor.

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

0.41mins
Q17a

Factor.

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

0.28mins
Q17b

Factor.

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

0.30mins
Q17c

Factor.

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

0.28mins
Q17d

Factor.

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

0.36mins
Q17e

Factor.

 \displaystyle 9g^2 + 4g - 10 

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.

3.30mins
Q18

Factor.

 \displaystyle x^2 - 49 

0.18mins
Q19a

Factor.

 \displaystyle y^2 - 121 

0.11mins
Q19b

Factor.

 \displaystyle 4k^2 - 9 

0.18mins
Q19c

Factor.

 \displaystyle 16 - 144a^2 

0.42mins
Q19d

Factor.

 \displaystyle 9w^2 -25x^2 

0.26mins
Q19e

Factor.

 \displaystyle 1 - 81p^2 

0.21mins
Q19f

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

 \displaystyle x^2 + 14x + 49 

0.32mins
Q20a

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

 \displaystyle k^2 + 8k + 16 

0.19mins
Q20b

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

 \displaystyle y^2 - 10y + 25 

0.21mins
Q20c

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

 \displaystyle 25y^2 -70y + 49 

0.27mins
Q20d

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

 \displaystyle 36c^2 - 108c + 81 

0.25mins
Q20e

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

 \displaystyle 121 +176y + 64y^2 

0.21mins
Q20f

Determine all values of k so that each trinomial is a perfect square.

25y2 + ky + 144

0.29mins
Q21a

Determine all values of k so that each trinomial is a perfect square.

9x^2 - 42x + k

0.41mins
Q21b

Factor, if possible.

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

0.31mins
Q22a

Factor, if possible.

 \displaystyle 625 - (y -5)^2 

1.09mins
Q22b

Factor, if possible.

 \displaystyle 144a^4 - 499b^4 

 \displaystyle 25x^2 + 30x + 4