6.3 Multiply polynomials  (Page 3/3)

$4(w+10)$

$6(b+8)$

$\mathrm{-3}(a+7)$

$\mathrm{-5}(p+9)$

$2(x-7)$

$7(y-4)$

$\mathrm{-3}(k-4)$

$\mathrm{-8}(j-5)$

$q(q+5)$

$k(k+7)$

$\text{−}b(b+9)$

$\text{−}y(y+3)$

$\text{−}x(x-10)$

$\text{−}p(p-15)$

$6r(4r+s)$

$5c(9c+d)$

$12x(x-10)$

$9m(m-11)$

$\mathrm{-9}a(3a+5)$

$\mathrm{-4}p(2p+7)$

$3(p^2+10p+25)$

$6(y^2+8y+16)$

$\mathrm{-8}x(x^2+2x-15)$

$\mathrm{-5}t(t^2+3t-18)$

$5q^3\left(q^3-2q+6\right)$

$4x^3\left(x^4-3x+7\right)$

$\mathrm{-8}y(y^2+2y-15)$

$\mathrm{-5}m(m^2+3m-18)$

$5q^3(q^2-2q+6)$

$9r^3(r^2-3r+5)$

$\mathrm{-4}{z}^2(3z^2+12z-1)$

$\mathrm{-3}{x}^2(7x^2+10x-1)$

$(2m-9)m$

$(8j-1)j$

$(w-6)·8$

$(k-4)·5$

$4(x+10)$

$6(y+8)$

$15(r-24)$

$12(v-30)$

$\mathrm{-3}(m+11)$

$\mathrm{-4}(p+15)$

$\mathrm{-8}(z-5)$

$\mathrm{-3}(x-9)$

$u(u+5)$

$q(q+7)$

$n(n^2-3n)$

$s(s^2-6s)$

$6x(4x+y)$

$5a(9a+b)$

$5p(11p-5q)$

$12u(3u-4v)$

$3(v^2+10v+25)$

$6(x^2+8x+16)$

$2n(4n^2-4n+1)$

$3r(2r^2-6r+2)$

$\mathrm{-8}y(y^2+2y-15)$

$\mathrm{-5}m(m^2+3m-18)$

$5q^3(q^2-2q+6)$

$9r^3(r^2-3r+5)$

$\mathrm{-4}{z}^2(3z^2+12z-1)$

$\mathrm{-3}{x}^2(7x^2+10x-1)$

$(2y-9)y$

$(8b-1)b$

$(w+5)(w+7)$

$(y+9)(y+3)$

$(p+11)(p-4)$

$(q+4)(q-8)$

$(x+8)(x+3)$

$(y+7)(y+4)$

$(y-6)(y-2)$

$(x-7)(x-2)$

$(w-4)(w+7)$

$(q-5)(q+8)$

$(p+12)(p-5)$

$(m+11)(m-4)$

$(6p+5)(p+1)$

$(7m+1)(m+3)$

$(2t-9)(10t+1)$

$(3r-8)(11r+1)$

$\left(5x-y\right)\left(3x-6\right)$

$\left(10a-b\right)\left(3a-4\right)$

$(a+b)(2a+3b)$

$(r+s)(3r+2s)$

$(4z-y)(z-6)$

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

$(x^2+3)(x+2)$

$(y^2-4)(y+3)$

$(x^2+8)(x^2-5)$

$(y^2-7)(y^2-4)$

$(5ab-1)(2ab+3)$

$(2xy+3)(3xy+2)$

$(6pq-3)(4pq-5)$

$(3rs-7)(3rs-4)$

$(x+5)(x^2+4x+3)$

$(u+4)(u^2+3u+2)$

$(y+8)(4y^2+y-7)$

$(a+10)(3a^2+a-5)$

$(w-7)(w^2-9w+10)$

$(p-4)(p^2-6p+9)$

$(3q+1)(q^2-4q-5)$

$(6r+1)(r^2-7r-9)$

$\left(10y-6\right)+\left(4y-7\right)$

$\left(15p-4\right)+\left(3p-5\right)$

$\left(x^2-4x-34\right)-\left(x^2+7x-6\right)$

$\left(j^2-8j-27\right)-\left(j^2+2j-12\right)$

$5q(3q^2-6q+11)$

$8t(2t^2-5t+6)$

$\left(s-7\right)\left(s+9\right)$

$\left(x-5\right)\left(x+13\right)$

$\left(y^2-2y\right)\left(y+1\right)$

$\left(a^2-3a\right)\left(4a+5\right)$

$\left(3n-4\right)\left(n^2+n-7\right)$

$\left(6k-1\right)\left(k^2+2k-4\right)$

$\left(7p+10\right)\left(7p-10\right)$

$\left(3y+8\right)\left(3y-8\right)$

$(4m^2-3m-7)m^2$

$(15c^2-4c+5)c^4$

$\left(5a+7b\right)\left(5a+7b\right)$

$\left(3x-11y\right)\left(3x-11y\right)$

$\left(4y+12z\right)\left(4y-12z\right)$

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 13 times 15. Think of 13 as $10+3$ and 15 as $10+5$ .

1. ⓐ Multiply $(10+3)(10+5)$ by the FOIL method.
2. ⓑ Multiply $13·15$ without using a calculator.
3. ⓒ Which way is easier for you? Why?

Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as $20-2$ and 17 as $20-3$ .

1. ⓐ Multiply $(20-2)(20-3)$ by the FOIL method.
2. ⓑ Multiply $18·17$ without using a calculator.
3. ⓒ Which way is easier for you? Why?

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

Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?

Multiply the following:

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

Explain the pattern that you see in your answers.

Multiply the following:

$\begin{array}{c}(m-3)(m+3)\hfill \\ (n-10)(n+10)\hfill \\ (p-8)(p+8)\hfill \end{array}$

Explain the pattern that you see in your answers.

Multiply the following:

$\begin{array}{c}(p+3)(p+3)\hfill \\ (q+6)(q+6)\hfill \\ (r+1)(r+1)\hfill \end{array}$

Explain the pattern that you see in your answers.

Multiply the following:

$\begin{array}{c}(x-4)(x-4)\hfill \\ (y-1)(y-1)\hfill \\ (z-7)(z-7)\hfill \end{array}$

Explain the pattern that you see in your answers.