Chapter 6

ⓐ monomial ⓑ polynomial ⓒ trinomial ⓓ binomial ⓔ monomial

ⓐ binomial ⓑ trinomial ⓒ monomial ⓓ polynomial ⓔ monomial

ⓐ $1$ ⓑ $4$ ⓒ $12$ ⓓ 3 ⓔ 0

ⓐ $0$ ⓑ $5$ ⓒ $1$ ⓓ 2 ⓔ 3

$21q^2$

$\mathrm{-7}{c}^2$

$13m$

$\mathrm{-10}{z}^3$

$5y^2+3z^2$

$\mathrm{-4}{m}^2+n^2$

There are no like terms to combine.

There are no like terms to combine.

$8x^2-11x+1$

$17y^2+14y+1$

$15x^2+3x-5$

$6b^2+3$

$2z^2+12z-2$

$5x^2+14x+7$

$5x^2-5xy+5y^2$

$7x^2-6xy-2y^2$

$\mathrm{-5}ab-5b^2$

$4n^2+7mn$

$x^3-y^3$

$p^3-2p^{2}q+q^3$

ⓐ $18$ ⓑ $50$ ⓒ $\mathrm{-15}$

ⓐ $18$ ⓑ $\mathrm{-4}$ ⓒ $14$

$250$

$106$

$576

$750

ⓐ 216 ⓑ $15$ ⓒ $\frac{9}{49}$ ⓓ 0.1849

ⓐ $32$ ⓑ 21 ⓒ $\frac{8}{125}$ ⓓ $0.047524$

ⓐ $81$ ⓑ $\mathrm{-81}$

ⓐ $169$ ⓑ $\mathrm{-169}$

$b^{17}$

$x^{16}$

ⓐ $5^6$ ⓑ $4^{18}$

ⓐ $7^{14}$ ⓑ ${10}^{11}$

ⓐ $p^6$ ⓑ $y^{43}$

ⓐ $z^8$ ⓑ $b^{49}$

$x^{18}$

$b^{19}$

ⓐ $b^{35}$ ⓑ $5^{12}$

ⓐ $z^{54}$ ⓑ $3^{49}$

ⓐ $144y^2$ ⓑ $32w^5{x}^5$

ⓐ $125w^3{x}^3$ ⓑ $\mathrm{-27}{y}^3$

ⓐ $a^{48}$ ⓑ $\mathrm{-8}{c}^{12}{d}^6$

ⓐ $81x^{24}{y}^{28}$ ⓑ $q^{29}$

ⓐ $75n^{12}$ ⓑ $81c^{24}{d}^{30}$

ⓐ $256a^{22}{b}^{24}$ ⓑ $40x^{10}$

$\mathrm{-35}{y}^{11}$

$54b^9$

$6a^5{b}^6$

$8r^{11}{s}^8$

$5x+35$

$3y+39$

$x^2-7x$

$d^2-11d$

$5x^2+20xy$

$12p^2+2pr$

$\mathrm{-15}{y}^3-24y^2+21y$

$8x^4-24x^3+20x^2$

$12x^3-20x^2+12x$

$\mathrm{-18}{a}^5+12a^4-36a^3$

$xp+8p$

$ap+4p$

$x^2+17x+72$

$20x^2+51x+27$

$12b^2+38b+30$

$a^2+17a+70$

$30y^2-3y-6$

$15c^2+14c-8$

$a^2-ab+7a-7b$

$x^2-xy+5x-5y$

$x^2+14x+48$

$y^2+20y+51$

$x^2-2x-35$

$b^2+3b-18$

$15x^2+29x-14$

$16y^2-20y-50$

$10c^2-60c-cd+6d$

$14x^2-35x-2xy+10y$

$x^3-8x^2+6x-48$

$y^3-9y^2+7y-63$

$8a^2{b}^2+12ab-20$

$8x^2{y}^2+2xy-15$

$15m^2-51m+42$

$42b^2-53b+15$

$y^3-8y^2+17y-6$

$2x^3+5x^2-7x+20$

$y^3-8y^2+17y-6$

$2x^3+5x^2-7x+20$

$x^2+18x+81$

$y^2+22y+121$

$x^2-18x+81$

$p^2-26p+169$

$36x^2+36x+9$

$16x^2+72x+81$

$4c^2-4cd+d^2$

$16x^2-40xy+25y^2$

$4x^4+4x^2+1$

$9y^6+12y^3+4$

$x^2-25$

$w^2-9$

$36x^2-25$

$4x^2-49$

$49-16x^2$

$81-4y^2$

$16p^2-49q^2$

$9x^2-y^2$

$x^2{y}^2-36$

$a^2{b}^2-81$

$9x^4-16y^6$

$4m^4-25n^6$

ⓐ FOIL; $18b^2+77b-18$ ⓑ Binomial Squares; $81p^2-72p+16$ ⓒ Binomial Squares; $49y^2+14y+1$ ⓓ Product of Conjugates; $16r^2-9$

ⓐ Binomial Squares; $36x^2+84x+49$ ⓑ Product of Conjugates; $9x^2-16$ ⓒ FOIL; $10x^2-29x+10$ ⓓ Binomial Squares; $36n^2-12n+1$

ⓐ $x^5$ ⓑ $6^9$

ⓐ $y^6$ ⓑ ${10}^8$

ⓐ $\frac{1}{x^4}$ ⓑ $\frac{1}{{12}^{15}}$

ⓐ $\frac{1}{m^8}$ ⓑ $\frac{1}{9^{11}}$

ⓐ $b^8$ ⓑ $\frac{1}{z^6}$

ⓐ $\frac{1}{p^8}$ ⓑ $w^4$

ⓐ 1 ⓑ 1

ⓐ 1 ⓑ 1

ⓐ $1$ ⓑ $1$

ⓐ $1$ ⓑ $1$

ⓐ $\frac{25}{64}$ ⓑ $\frac{p^4}{\mathrm{10,000}}$ ⓒ $\frac{m^7}{n^7}$

ⓐ $\frac{1}{27}$ ⓑ $\frac{\mathrm{-8}}{q^3}$ ⓒ $\frac{w^4}{x^4}$

$m^{13}$

$k^5$

1

1

$r^8$

$v^6$

$\frac{a^{12}}{b^8}$

$\frac{q^{21}}{r^{15}}$

$\frac{49x^6}{81y^2}$

$\frac{9x^8}{49y^2}$

$\frac{1}{a^6}$

$\frac{1}{p^{15}}$

$9r^{18}$

$\frac{2}{x}$

$7y^6$

$6z^6$

$-\frac{9}{a^{5}b}$

$\frac{\mathrm{-9}d}{c^4}$

$\frac{2a^6}{3b^2}$

$-\frac{3q^6}{5p^8}$

$\frac{4y^2}{7x^4}$

$\frac{5}{8m^5{n}^3}$

$2a{b}^2$

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

$2z^2+6$

$2z^2-3$

$9b^2-11b$

$5y^2-11y$

$\mathrm{-5}{y}^2+3y$

$\mathrm{-7}{b}^2+3b$

$15d^4+6d^2$

$36p^4-8p^2$

$\mathrm{-4}a+2b$

$8a^{5}b+6a^3{b}^2$

$5xy+3y-2y^2$

$5a^2+2a^{2}b-6b^2$

$3c+1-\frac{3}{2c}$

$2d-1-\frac{2}{5d}$

$y+7$

$m+5$

$2x+5$

$3x+2$

$x^2+3x+2+\frac{2}{x+2}$

$2x^2+6x-5-\frac{3}{x+1}$

$x^2-2x+7$

$x^3-8x^2+40x-200$

$x^2+4x+16$

$25x^2+10x+4$

ⓐ $\frac{1}{8}$ ⓑ $\frac{1}{{10}^7}$

ⓐ $\frac{1}{9}$ ⓑ $\frac{1}{\mathrm{10,000}}$

ⓐ $p^8$ ⓑ $64$

ⓐ $q^7$ ⓑ $16$

ⓐ $\frac{81}{16}$ ⓑ $\frac{n^2}{36m^2}$

ⓐ $\frac{125}{27}$ ⓑ $\frac{16b^4}{a^4}$

ⓐ $\frac{1}{25}$ ⓑ $-\frac{1}{25}$ ⓒ 25 ⓓ $\mathrm{-25}$

ⓐ $\frac{1}{49}$ ⓑ $-\frac{1}{49}$ ⓒ 49 ⓓ $\mathrm{-49}$

ⓐ $2$ ⓑ $\frac{1}{18}$

ⓐ 2 ⓑ $\frac{1}{256}$

ⓐ $\frac{1}{y^7}$ ⓑ $\frac{1}{z^{15}}$

ⓐ $\frac{1}{p^9}$ ⓑ $\frac{1}{q^{24}}$

ⓐ $\frac{8}{p}$ ⓑ $\frac{1}{8p}$ ⓒ $-\frac{1}{8p}$

ⓐ $\frac{1}{11q}$ ⓑ $\frac{1}{11q}$$-\frac{1}{11q}$ ⓒ $-\frac{11}{q}$

ⓐ $x^4$ ⓑ $\frac{1}{y^5}$ ⓒ $\frac{1}{z^9}$

ⓐ $a^5$ ⓑ $\frac{1}{b^4}$ ⓒ $\frac{1}{c^{15}}$

$\frac{1}{p^3{q}^3}$

$\frac{1}{r^2{s}^8}$

$-\frac{12v^5}{u}$

$\frac{30d^3}{c^8}$

$\frac{1}{16x^8}$

$\frac{1}{16b^{12}}$

$\frac{64}{a^8}$

$\frac{8}{c^{12}}$

$x^{11}$

$y^{14}$

$9.6\times {10}^4$

$4.83\times {10}^4$

$7.8\times {10}^{\mathrm{-3}}$

$1.29\times {10}^{\mathrm{-2}}$

1,300

92,500

0.00012

0.075

0.06

0.009

400,000

20,000

ⓐ trinomial ⓑ polynomial ⓒ binomial ⓓ monomial ⓔ binomial

ⓐ binomial ⓑ trinomial ⓒ polynomial ⓓ trinomial ⓔ monomial

ⓐ 2 ⓑ 4 ⓒ 1 ⓓ 3 ⓔ 0

ⓐ 1 ⓑ 2 ⓒ 3 ⓓ 3 ⓔ 0

$12x^2$

$6w$

$\mathrm{-5}a$

$40x$

$\mathrm{-22}b$

$\text{−10a}+5b$

$\mathrm{-4}{a}^2+b^2$

$x{y}^2-5x-5y^2$

$a^{2}b-4a-5a{b}^2$

$\text{12a}+8b$

$\mathrm{-4}a-3b$

$\mathrm{-17}{x}^6$

$11y^2+4y+11$

$\mathrm{-3}{x}^2+17x-1$

$11x^2-5x+5$

$6a^2-4a-1$

$2m^2-7m+4$

$5a+3$

$12s^2-16s+9$

$3x^2-x+4$

$w^2+3w+4$

$2p^3+p^2+9p+10$

$8a^3+a^2-2a+12$

$11w-66$

$12c-45$

$10x^2-7xy+6y^2$

$10m^2+3mn-8n^2$

$\mathrm{-3}ab+3b^2$

$4uv+2v^2$

$p^3-6p^{2}q+p{q}^2+4q^3$

$x^3+2x^{2}y-5x{y}^2+y^3$

ⓐ 187 ⓑ 46 ⓒ 2

ⓐ −104 ⓑ 4 ⓒ 40

11

$10,800

4

$58

149

Answers will vary.

Answers will vary.

ⓐ 10,000 ⓑ 17 ⓒ $\frac{4}{81}$ ⓓ 0.125

ⓐ 512 ⓑ 8 ⓒ $\frac{27}{64}$
ⓓ 0.064

ⓐ 64 ⓑ $\mathrm{-64}$

ⓐ $-\frac{4}{9}$
ⓑ $\frac{4}{9}$

ⓐ $\mathrm{-0.0001}$ ⓑ 0.0001

$x^6$

$q^{42}$

ⓐ $3^{16}$ ⓑ $5^5$

ⓐ $w^6$ ⓑ $u^{94}$