# Multiply and simplify: (2 x + 5 y)(3 x^2 - 4 x y + 2 y^2).

## Question:

Multiply and simplify: {eq}(2 x + 5 y)(3 x^2 - 4 x y + 2 y^2) {/eq}.

## Distributive Property of Multiplication:

When multiplying expressions, the product would often be the sum of all of the products. FOr example a monomial is multiplied to a polynomial, the monomial will be multiplied to each term of the polynomial such that {eq}a(b + c + d) = ab +ac+ad {/eq} Collecting like terms and following the mathematical operations would then simplify the product.

Distribute the binomial:

{eq}(2 x + 5 y)(3 x^2 - 4 x y + 2 y^2) {/eq}

{eq}(2 x)(3 x^2 - 4 x y + 2 y^2) + (5 y)(3 x^2 - 4 x y + 2 y^2) {/eq}

{eq}(2 x)(3 x^2) - (2 x)(4 x y) + (2 x)(2 y^2) + (5 y)(3 x^2) - (5 y)(4 x y) +(5 y)( 2 y^2) {/eq}

Evaluating and collecting like terms:

{eq}6 x^3 - 8 x^2 y + 4 x y^2 + 15 x^2y - 29 x y^2 +10y^3 {/eq}

{eq}6 x^3 - 8 x^2 y + 15 x^2y + 4 x y^2 - 29 x y^2 +10y^3 {/eq}

{eq}6 x^3 + 7 x^2y - 25 x y^2 +10y^3 {/eq}

The expression {eq}(2 x + 5 y)(3 x^2 - 4 x y + 2 y^2) {/eq} when simplified is {eq}6 x^3 + 7 x^2y - 25 x y^2 +10y^3 {/eq}. 