Question

enter the correct answer in the box.

simplify the polynomial expressions by combining like terms, then find their product.

\\(6x - 9 - 2x)(8 + 5x - 5)\\

Explanation:

⚡ Using what you learned: multiplying polynomials · adding and subtracting polynomials

Step 1: Simplify individual factors

Combine like terms inside each set of parentheses first:

First factor:

$$ (6x - 9 - 2x) = (6x - 2x) - 9 = 4x - 9 $$

Second factor:

$$ (8 + 5x - 5) = 5x + (8 - 5) = 5x + 3 $$

The expression becomes:

$$ (4x - 9)(5x + 3) $$

Step 2: Multiply the simplified binomials

Multiply the terms using the distributive property (FOIL method):

$$ (4x)(5x) + (4x)(3) + (-9)(5x) + (-9)(3) $$

$$ = 20x^2 + 12x - 45x - 27 $$

Step 3: Combine like terms

Combine the middle \(x\) terms:

$$ 12x - 45x = -33x $$

So, the simplified product is:

$$ 20x^2 - 33x - 27 $$

Answer:

$$ 20x^2 - 33x - 27 $$