Question

Here are five sums. Use the distributive property to write each sum as a product with two factors. 2+7 5−10 −2^2 +++ 2−1/2

Answer 1

Question:

Here are five sums. Use the distributive property to write each sum as a product with two factors.

$(a)\ 2a + 7a$      $(b)\ 5z - 10$    $(c)\ c - c^2$      $(d)\ r + r+ r+ r$    $(e)\ 2x - \frac{1}{2}$

Answer:

$(a)\ 2a + 7a = 9a$

$(b)\ 5z - 10 = 5(z - 2)$

$(c)\ c - c^2 = c(1 - c)$

$(d)\ r + r + r + r = 4r$

$(e)\ 2x - \frac{1}{2} = \frac{1}{2}(4x - 1)$

Step-by-step explanation:

Required

Apply distributive property

$(a)\ 2a + 7a$      

Apply distributive property [Factor out a]

$2a + 7a = a(2 + 7)$

$2a + 7a = a(9)$

Open bracket

$2a + 7a = a*9$

$2a + 7a = 9a$

$(b)\ 5z - 10$    

Express 10 as 5 * 2

$5z - 10 = 5z - 5*2$

Apply distributive property [Factor out 5]

$5z - 10 = 5(z - 2)$

$(c)\ c - c^2$      

Express c as c * c

$c - c^2 = c - c * c$

Apply distributive property [Factor out c]

$c - c^2 = c(1 - c)$

$(d)\ r + r+ r+ r$    

Express r as r * 1

$r + r + r + r = r * 1 + r * 1 + r * 1 + r *1$

Apply distributive property [Factor out 1]

$r + r + r + r = r(1+1+1+1)$

$r + r + r + r = r * 4$

$r + r + r + r = 4r$

$(e)\ 2x - \frac{1}{2}$

Express 2x as 4x/2

$2x - \frac{1}{2} = \frac{4x}{2} - \frac{1}{2}$

Apply distributive property [Factor out 1/2]

$2x - \frac{1}{2} = \frac{1}{2}(4x - 1)$