Question

multiply the polynomials using the distributive property and combine like terms.

\\((2x + 2)(3x - 5)\\)

Explanation:

Identify the given expression

We are given two binomials to multiply:

$$ (2x + 2)(3x - 5) $$

Our goal is to expand this expression using the distributive property and simplify by combining like terms.

Apply the distributive property

Using Polynomial Multiplication and the Distributive Property with Polynomials, we distribute each term in the first binomial to each term in the second binomial:

$$ (2x + 2)(3x - 5) = 2x(3x - 5) + 2(3x - 5) $$

Expand the distributed terms

Now, we multiply the terms inside each set of parentheses:

$$ 2x(3x) + 2x(-5) + 2(3x) + 2(-5) $$

$$ = 6x^2 - 10x + 6x - 10 $$

Combine like terms

Using Polynomial Simplification, we group and combine the linear terms (\(x\)-terms):

$$ -10x + 6x = (-10 + 6)x = -4x $$

Substituting this back gives the simplified polynomial:

$$ 6x^2 - 4x - 10 $$

Answer:

\(6x^2 - 4x - 10\)