## Elementary Algebra

$-32x^3+2xy^2$
Using $(a-b)(a+b)=a^2-b^2$, or the product of the sum and difference of like terms, the given expression, $-2x(4x+y)(4x-y) ,$ is equivalent to \begin{array}{l}\require{cancel} -2x[(4x)^2-(y)^2] \\\\= -2x(16x^2-y^2) .\end{array} Using the Distributive Property, the expression, $-2x(16x^2-y^2) ,$ is equivalent to \begin{array}{l}\require{cancel} -32x^3+2xy^2 .\end{array}