Question

question 8 of 10, step 1 of 1
determine ( g(x + a) - g(x) ) for the following function.
( g(x) = -3x^2 + 5x )
answer
( g(x + a) - g(x) = )
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Explanation:

Step1: Compute $g(x+a)$

Substitute $x+a$ into $g(x)$:
$$g(x+a) = -3(x+a)^2 + 5(x+a)$$
Expand the expression:
$$g(x+a) = -3(x^2+2ax+a^2) + 5x+5a = -3x^2-6ax-3a^2+5x+5a$$

Step2: Subtract $g(x)$ from $g(x+a)$

Substitute $g(x) = -3x^2+5x$ and simplify:
$$g(x+a)-g(x) = (-3x^2-6ax-3a^2+5x+5a) - (-3x^2+5x)$$
$$= -3x^2-6ax-3a^2+5x+5a+3x^2-5x$$

Step3: Combine like terms

Cancel and simplify remaining terms:
$$= -6ax -3a^2 +5a$$

Answer:

$\boldsymbol{-3a^2 -6ax +5a}$ (or factored as $\boldsymbol{a(-3a-6x+5)}$)