다항식의 연산

$(s-7)(s+9)$

$({y}^{2}-2y)(y+1)$

$(5x-y)(x-4)$

$(6k-1)({k}^{2}+2k-4)$

$(3x-11y)(3x-11y)$

$(11-b)(11+b)$

$\left(rs-\frac{2}{7}\right)\left(rs+\frac{2}{7}\right)$

$(2{x}^{2}-3{y}^{4})(2{x}^{2}+3{y}^{4})$

${(m-15)}^{2}$

${(3d+1)}^{2}$

${(4a+10)}^{2}$

${\left(3z+\frac{1}{5}\right)}^{2}$

Multiply Polynomial Functions

For functions $f(x)=x+2$ and $g(x)=3{x}^{2}-2x+4,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(-1)$

Multiply Polynomial Functions

For functions $f(x)=x-1$ and $g(x)=4{x}^{2}+3x-5,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(-2)$

Multiply Polynomial Functions

For functions $f(x)=2x-7$ and $g(x)=2x+7,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(-3)$

Multiply Polynomial Functions

For functions $f(x)=7x-8$ and $g(x)=7x+8,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(-2)$

Multiply Polynomial Functions

For functions $f(x)={x}^{2}-5x+2$ and $g(x)={x}^{2}-3x-1,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(-1)$

Multiply Polynomial Functions

For functions $f(x)={x}^{2}+4x-3$ and $g(x)={x}^{2}+2x+4,$ find ⓐ $(f\cdot g)(x)$ ⓑ $(f\cdot g)(1)$

Which method do you prefer to use when multiplying two binomials: the Distributive Property or the FOIL method? Why? Which method do you prefer to use when multiplying a polynomial by a polynomial: the Distributive Property or the Vertical Method? Why?

Multiply the following:

$\begin{array}{c}(x+2)(x-2) \\ (y+7)(y-7) \\ (w+5)(w-5)\end{array}$

Explain the pattern that you see in your answers.