Question

Which of the following expressions is equivalent to (x-2)(3x - 8)+(x - 2)(4x + 3)?

A) (x-2)(7x - 5)
B) (x-2)(7x - 11)
C) (x-2)(7x - 6)
D) (x-2)(7x + 1)

Answer 1

To simplify the given expression, use the distributive property and combine like terms.

Step-by-step explanation:

To simplify the given expression, we need to apply the distributive property. The distributive property states that for any three real numbers a, b, and c, a(b + c) = ab + ac. In this case, we have (x-2)(3x - 8)+(x - 2)(4x + 3). Applying the distributive property:

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

Now, we can simplify each of these expressions:

3x(x-2) = 3x^2 - 6x

-8(x-2) = -8x + 16

4x(x-2) = 4x^2 - 8x

3(x-2) = 3x - 6

Substituting these simplified expressions back into the original equation:

(x-2)(3x - 8)+(x - 2)(4x + 3) = 3x^2 - 6x - 8x + 16 + 4x^2 - 8x + 3x - 6

Combining like terms:

7x^2 - 14x + 10