Question

ynomials using the distributive property and combine like terms.

\\(x + 8)(x + 6)\\

Explanation:

Apply the distributive property

To multiply the binomials, we distribute each term of the first polynomial to each term of the second polynomial. This is also known as the FOIL Method or Polynomial Multiplication.

$$ (x + 8)(x + 6) = x(x + 6) + 8(x + 6) $$

Expand the terms

We now apply the Distributive Property with Polynomials to expand both parts of the expression.

$$ x(x + 6) + 8(x + 6) = (x \cdot x) + (x \cdot 6) + (8 \cdot x) + (8 \cdot 6) $$

$$ = x^2 + 6x + 8x + 48 $$

Combine like terms

To simplify the expression, we perform Polynomial Simplification by grouping and adding the coefficients of the like terms, which are \(6x\) and \(8x\).

$$ x^2 + (6 + 8)x + 48 = x^2 + 14x + 48 $$

Answer:

Multiply the binomials using the distributive property and combine like terms.

$$(x + 8)(x + 6) =$$

<blank>\(x^2 + 14x + 48\)</blank>