Question

multiply and simplify, if necessary.

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

Explanation:

Distribute the first term

Using the Multiplying Monomial by Polynomial and Distributive Property with Polynomials knowledge points

$$ 3x(5x + 2) = 3x \cdot 5x + 3x \cdot 2 = 15x^2 + 6x $$

Distribute the second term

Using the Distributive Property with Polynomials knowledge point

$$ 2(5x + 2) = 2 \cdot 5x + 2 \cdot 2 = 10x + 4 $$

Combine the distributed expressions

Using the Polynomial Addition knowledge point

$$ (15x^2 + 6x) + (10x + 4) = 15x^2 + 6x + 10x + 4 $$

Simplify by combining like terms

Using the Polynomial Simplification knowledge point

$$ 15x^2 + (6x + 10x) + 4 = 15x^2 + 16x + 4 $$

Answer:

\(15x^2 + 16x + 4\)