Simplify the product:
2x−7

x+8
⋅4x(x−8)(x+8). Leave in factored form.

Question

Simplify the product: 
2x−7

x+8
⋅4x(x−8)(x+8). Leave in factored form.

BlackTom AI · Accepted Answer

To simplify the given product, start by identifying the two factors: (2x − 7)/(x + 8) and 4x(x − 8)(x + 8).

Notice that (x + 8) appears in both the numerator of the first fraction and as a factor in the second expression. Since we are multiplying these expressions, these common factors cancel: (2x − 7)/(x + 8) × 4x(x − 8)(x + 8) = (2x − 7) × 4x(x − 8) × [(x + 8)/(x + 8)].

The (x + 8) terms cancel, leaving 4x(2x − 7)(x − 8).

Thus, the product simplifies to 4x(2x − 7)(x − 8) in factored form.

If you prefer, you can rearrange the factors in any order, since multiplication is commutative; however, the factorization 4x(2x − 7)(x − 8) is already in a clean, factored form.

ALGII141-027 5.2 Practice Problems

Simplify the product: 2x−7 x+8 ⋅4x(x−8)(x+8). Leave in factored form.

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