## Intermediate Algebra (12th Edition)

$4y^2-9z^2+6xz-x^2$
Use special products to multiply the given expression, $[2y+(3z-x)][2y-(3z-x)] .$ Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the product of the expression above is \begin{array}{l}\require{cancel} (2y)^2-(3z-x)^2 \\\\= 4y^2-(3z-x)^2 .\end{array} Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the product of the expression above is \begin{array}{l}\require{cancel} 4y^2-[(3z)^2+2(3z)(-x)+(-x)^2] \\\\= 4y^2-[9z^2-6xz+x^2] \\\\= 4y^2-9z^2+6xz-x^2 .\end{array}