Question

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Write an equivalent expression using distributive property and simplify for each question

A. 2x+10x
B. -4(3x-10)+5(2-6x)
C. 2(x-4)+x
D. -3-7(3-4x)+8x

Answer 1

A) 2 x + 10 x = 2x ( 1 + 5)

B) -4(3 x - 10)+5 (2 - 6 x) =2 ( -21 x + 25)

C) 2(x-4)+x = 3 x - 8

D) -3 -7(3 -4 x) + 8 x = 12 (3 x - 2)

Explanation:

DISTRIBUTIVE PROPERTY:

`A(B \pm C)  = AB \pm AC`

Now, here the given expressions are:

A. 2 x+ 10 x

Here, in 2 x + 10 x tale (2 x) as a common factor.

⇒2 x + 10 x = 2 x ( 1 + 5)

So, by distributive property: 2 x + 10 x = 2x ( 1 + 5)

B. -4(3 x - 10)+5 (2 - 6 x)

Here, solving the given expression, we get:

-4(3 x - 10)+5 (2 - 6 x) = -4(3 x) -4(-10) + 5(2) +5 (-6x)

= - 12 x + 40 + 10 - 30 x = -42 x + 50

Now, take (2) as common factor, we get: -42 x + 50 =2 ( -21 x + 25)

So, by distributive property: -4(3 x - 10)+5 (2 - 6 x) =2 ( -21 x + 25)

C. 2(x-4)+x

Here, solving the given expression, we get:

2(x-4)+x = 2(x) - 2(4) + x = 2 x - 8 + x = 3 x - 8

Hence, 2(x-4)+x = 3 x - 8

D. -3-7(3-4x)+8x

Here, solving the given expression, we get:

-3-7(3-4x)+8x = -3 -(7(3) + 7(-4)) + 8 x = -3 - 21 + 28 x + 8 x = 36 x - 24

Now, take (12) as common factor, we get : 36 x - 24 = 12 (3 x - 2)

Hence -3 -7(3 -4 x) + 8 x = 12 (3 x - 2)