Expand and simplify.

\displaystyle -2 x(3 x-4)-x(x+6)

Expand and simplify.

\displaystyle -3(5 n-4)^{2}-5(5 n+4)^{2}

Expand and simplify.

\displaystyle -8\left(x^{2}-5 x+7\right)+5(2 x-5)(3 x-7)

Expand and simplify.

\displaystyle -3(5 a-4)(5 a+4)-3 a(a-7)

What two binomials are being multiplied and what is the product?

\displaystyle \begin{array}{|c|c|c|r|r|r|}\hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x^{2} & x^{2} & x^{2} & -x & -x & -x \\ \hline x^{2} & x^{2} & x^{2} & -x & -x & -x \\ \hline\end{array}

A rectangle has a width of \displaystyle 2 x-3 and a length of \displaystyle 3 x+1 . a) Write its area as a simplified polynomial. b) Write expressions for the dimensions if the width is doubled and the length is increased by \displaystyle 2 . c) Write the new area as a simplified polynomial.

Use pictures and words to show how to factor \displaystyle -2 x^{2}+8 x .

Factor.

\displaystyle x^{2}+x-12

Factor.

\displaystyle a^{2}+16 a+63

Factor.

\displaystyle -5 x^{2}+75 x-280

Factor.

\displaystyle y^{2}+3 y-54

Factor.

\displaystyle 2 x^{2}-9 x-5

Factor.

\displaystyle 12 n^{2}-67 n+16

Factor.

\displaystyle 6 x^{2}-15 x+6

Factor.

\displaystyle 8 a^{2}-14 a-15

What dimensions can a rectangle with an area of \displaystyle 12 x^{2}-3 x-15 have?

State all the integers, \displaystyle m , such that \displaystyle x^{2}+m x-13 can be factored.

Factor.

\displaystyle 121 x^{2}-25

Factor.

\displaystyle 36 a^{2}-60 a+25

Factor.

\displaystyle x^{4}-81

Factor.

\displaystyle (3-n)^{2}-12(3-n)+36

Determine all integers, \displaystyle m and \displaystyle n , such that \displaystyle m^{2}-n^{2}=45