Question

enter the correct answer in the box.

simplify the following expression.

\\(4x^2 + 8x + 15) + (x^2 - x - 27) - (x + 5)(x - 7)\\

Explanation:

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

Step 1: Multiply the binomials

$$ (x + 5)(x - 7) = x^2 - 7x + 5x - 35 = x^2 - 2x - 35 $$

Step 2: Rewrite the expression

$$ (4x^2 + 8x + 15) + (x^2 - x - 27) - (x^2 - 2x - 35) $$

Step 3: Distribute the negative sign

$$ 4x^2 + 8x + 15 + x^2 - x - 27 - x^2 + 2x + 35 $$

Step 4: Combine like terms

Group the \(x^2\) terms, \(x\) terms, and constant terms:

$$ (4x^2 + x^2 - x^2) + (8x - x + 2x) + (15 - 27 + 35) $$

$$ 4x^2 + 9x + 23 $$

Answer:

\(4x^2 + 9x + 23\)