10.6 Introduction to factoring polynomials  (Page 5/6)

${(3^2)}^5$

${(a^{10})}^y$

${(8n)}^2$

${(\mathrm{-5}x)}^3$

${(2ab)}^8$

${(\mathrm{-10}mnp)}^4$

${(3a^5)}^3$

${(4y)}^2(8y)$

${(x^3)}^5{(x^2)}^3$

${(5s{t}^2)}^3{(2s^3{t}^4)}^2$

Multiply Monomials

In the following exercises, multiply the monomials.

$(\mathrm{-6}{p}^4)(9p)$

$\left(\frac{1}{3}{c}^2\right)\left(30c^8\right)$

$(8x^2{y}^5)(7x{y}^6)$

$\left(\frac{2}{3}{m}^3{n}^6\right)\left(\frac{1}{6}{m}^4{n}^4\right)$

$7(10-x)$

$a^2(a^2-9a-36)$

$\mathrm{-5}y(125y^3-1)$

$(4n-5)(2n^3)$

$(a+5)(a+2)$

$(y-4)(y+12)$

$(3x+1)(2x-7)$

$(6p-11)(3p-10)$

$(n+8)(n+1)$

$(k+6)(k-9)$

$(5u-3)(u+8)$

$(2y-9)(5y-7)$

$(p+4)(p+7)$

$(x-8)(x+9)$

$(3c+1)(9c-4)$

$(10a-1)(3a-3)$

$(x+1)(x^2-3x-21)$

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

$(m+6)(m^2-7m-30)$

$(4y-1)(6y^2-12y+5)$

$\frac{2^8}{2^2}$

$\frac{a^6}{a}$

$\frac{n^3}{n^{12}}$

$\frac{x}{x^5}$

$3^0$

$y^0$

${(14t)}^0$

$12a^0-15b^0$

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

${\left(\frac{x}{2}\right)}^5$

${\left(\frac{5m}{n}\right)}^3$

${\left(\frac{s}{10t}\right)}^2$

$\frac{{(a^3)}^2}{a^4}$

$\frac{u^3}{u^2·u^4}$

${\left(\frac{x}{x^9}\right)}^5$

${\left(\frac{p^4·p^5}{p^3}\right)}^2$

$\frac{{(n^5)}^3}{{(n^2)}^8}$

${\left(\frac{5s^2}{4t}\right)}^3$

$72p^{12}÷8p^3$

$\mathrm{-26}{a}^8÷\left(2a^2\right)$

$\frac{45y^6}{\mathrm{-15}{y}^{10}}$

$\frac{\mathrm{-30}{x}^8}{\mathrm{-36}{x}^9}$

$\frac{28a^{9}b}{7a^4{b}^3}$

$\frac{11u^6{v}^3}{55u^2{v}^8}$

$\frac{\left(5m^9{n}^3\right)\left(8m^3{n}^2\right)}{\left(10m{n}^4\right)\left(m^2{n}^5\right)}$

$\frac{42r^2{s}^4}{6r{s}^3}-\frac{54r{s}^2}{9s}$

$6^{\mathrm{-2}}$

${\left(\mathrm{-10}\right)}^{\mathrm{-3}}$

$5·2^{\mathrm{-4}}$

${\left(8n\right)}^{\mathrm{-1}}$

$x^{\mathrm{-3}}·x^9$

$r^{\mathrm{-5}}·r^{\mathrm{-4}}$

$\left(u{v}^{\mathrm{-3}}\right)\left(u^{\mathrm{-4}}{v}^{\mathrm{-2}}\right)$

${\left(m^5\right)}^{\mathrm{-1}}$

${\left(k^{\mathrm{-2}}\right)}^{\mathrm{-3}}$

$\frac{q^4}{q^{20}}$

$\frac{b^8}{b^{\mathrm{-2}}}$

$\frac{n^{\mathrm{-3}}}{n^{\mathrm{-5}}}$

$\mathrm{5,300,000}$

$0.00814$

The thickness of a piece of paper is about $0.097$ millimeter.

According to www.cleanair.com, U.S. businesses use about $\mathrm{21,000,000}$ tons of paper per year.

$2.9\times {10}^4$

$1.5\times {10}^8$

$3.75\times {10}^{\mathrm{-1}}$

$9.413\times {10}^{\mathrm{-5}}$

$\left(3\times {10}^7\right)\left(2\times {10}^{\mathrm{-4}}\right)$

$\left(1.5\times {10}^{\mathrm{-3}}\right)\left(4.8\times {10}^{\mathrm{-1}}\right)$

$\frac{6\times {10}^9}{2\times {10}^{\mathrm{-1}}}$

$\frac{9\times {10}^{\mathrm{-3}}}{1\times {10}^{\mathrm{-6}}}$

$5n,45$

$8a,72$

$12x^2,20x^3,36x^4$

$9y^4,21y^5,15y^6$

$16u-24$

$15r+35$

$6p^2+6p$

$10c^2-10c$

$\mathrm{-9}{a}^5-9a^3$

$\mathrm{-7}{x}^8-28x^3$

$5y^2-55y+45$

$2q^5-16q^3+30q^2$

For the polynomial $8y^4-3y^2+1$

1. ⓐ Is it a monomial, binomial, or trinomial?
2. ⓑ What is its degree?

$(5a^2+2a-12)+(9a^2+8a-4)$

$(10x^2-3x+5)-(4x^2-6)$

${\left(-\frac{3}{4}\right)}^3$

$n·n^4$

${(10p^3{q}^5)}^2$

$(8x{y}^3)(\mathrm{-6}{x}^4{y}^6)$

$4u(u^2-9u+1)$

$\left(s+8\right)\left(s+9\right)$

$(m+3)(7m-2)$

$\left(11a-6\right)\left(5a-1\right)$

$(n-8)(n^2-4n+11)$

$(4a+9b)(6a-5b)$

$\frac{5^6}{5^8}$

${\left(\frac{x^3·x^9}{x^5}\right)}^2$

${(47a^{18}{b}^{23}{c}^5)}^0$

$\frac{24r^{3}s}{6r^2{s}^7}$

$\frac{8y^2-16y+20}{4y}$

$(15x{y}^3-35x^{2}y)÷5xy$

$4^{\mathrm{-1}}$

${\left(2y\right)}^{\mathrm{-3}}$

$p^{\mathrm{-3}}·p^{\mathrm{-8}}$

$\frac{x^4}{x^{\mathrm{-5}}}$

$80a^3+120a^2+40a$

$\mathrm{-6}{x}^2-30x$

According to www.cleanair.org, the amount of trash generated in the US in one year averages out to $\mathrm{112,000}$ pounds of trash per person. Write this number in scientific notation.

Convert $5.25\times {10}^{\mathrm{-4}}$ to decimal form.

$\left(2.4\times {10}^8\right)\left(2\times {10}^{\mathrm{-5}}\right)$

$\frac{9\times {10}^4}{3\times {10}^{\mathrm{-1}}}$

A hiker drops a pebble from a bridge $240$ feet above a canyon. The polynomial $\mathrm{-16}{t}^2+240$ gives the height of the pebble $t$ seconds a after it was dropped. Find the height when $t=3.$