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수와 식 5. 다음울 인 수분해하여라. 1. 다옴 전개에서 연산법칙이 어떻게 사용되었는지 알아보자. $a^{3}+b^{3}=a^{3}+a^{2}b-a^{2}b+$ $\left(x^{2}+x+1\right)\left(x^{2}-x+$ 1) $a^{2}\left(a+$ $b\right)-b\left(a^{2}-$ ) $a^{2}\left(a+$ $b\right)-b\left(a+$ $b\right)\left(a-b\right)$ $\left(x^{2}+1+x\right)$ $\left(x^{2}+1-x\right)$ ( $\left(a+b\right)\left(a^{2}-b\left(a-b\right)$ (at $b\right)\left(a^{2}-ab+$ $\left(x^{2}+1\right)^{2}-x3$ ( $\left(a+$ $b\right)\left(a-$ $b\right)=a^{2}$ b2) (1) $a^{3}-$ (2) $\left(a+b\right)^{3}+4$ $=$ x $+$ 2x2 $+1-x^{2}$ ( $\left(a+$ b)2 $=$ a2 $+2ab+$ b2) (3) $x^{3}+y^{3}+z^{3}$ $+2^{3}-3x$ yz (4) $a^{3}+3a^{2}b+3ab^{2}+b$ $x^{4}+2x^{2}-$ 1 ( ) $x^{4}+x^{2}+$ ( 동류항 계산 ) 6. 다음을 유리화 하여라. (1) $3\sqrt{2} +1$ (2) $3_{\sqrt{2} -1}$ (3) 4 2 다움을 전개하시오. 1) $\left(a+b+c$ $\left(a+b-c\right)$ (2) $\left(a+$ $b+c\right)$ $\left(a-b+c$ 7. 다음을 인 수분해하여라. 3) $\left(a+b+$ c) $\left(a-b-c$ (4) $\left(a+b-c\right)$ $1a$ $\left(a-b-c\right)$ 보기$2$ 5) $\left(a+b-c$ $1$ $\infty $ $g$ c) (6) $\left(a-b+c\right)$ $14$ $\left(a-b-c\right)$ 1 $y+$ 7) (x2 $+x-1\right)$ (x2 $-x-$ $-$ 1) (8) (x22x $+2x+2\right)\left($ $+$ $5$ $x^{2}+3xy+2y^{2}+y-$ ) $\left(x^{2}+2x-2\right)$ (x2 $2x=$ 2) (10) (x2 $+3x+1\right)\left(x^{2-3x+1}\right)$ $x^{2}+\left(3y\right)x+\left(2y-1\right)\left(y+$ 1) $2y-1$ $\left(x+$ $\left(y+1\right)$ $x+$ $\left(2y-1\right)$ 3y 1) $\left(x+y+1\right)$ $\left(x+y-1\right)$ $\left(x-y+$ 1) $\left(x-y-1\right)$ 2) $\left(x+$ a) $\left(x-a\right)$ (x2 ax $+$ a) (x $+ax+$ a2) $1\right)x^{2}+2xy+y^{2}-2x-2y+$ (2) $x^{2}+xy-2y^{2}-2x-y+1$ (3) $x^{2}-xy-2y^{2}-x-$ $7y-6$ (4) $x^{2}-xy-2y^{2}+5x-y+$ 다음을 인수분해하시오. ( X ) (5) $4c\left(b^{2}+1\right)+\left(a^{2}+$ c2)b ) $x^{4}+x^{2}$ $+1$ (2) $x^{4-6x^{2}}+1$ (6) $\left(a+b+$ $c\right)\left(ab+bc+$ ca) abc ) $x^{4-3x^{2}}$ (4) $x^{1-7x^{2}}+$ 1 (7) $\left(x+y\right)\left(y+z\right)\left(z+$ x) $+$ xyz O $x^{4-11x^{2}+}$ (6) 23x $3x^{2}+1$ (8) $x^{2-y^{2}+2yz+2zx+4x+2y+2z+}$ $x^{4}+4$ (8) $x^{4-13x^{2}}+4$ (9) $2x^{2}-7xy+6y^{2}+3x-4y-3$ (10) $x^{3}+2x^{2}y-x-2y$ 다음을 인수 분해하시오. (11) $a^{3}-a^{2}b-ac^{2}+bc\right)$ $\left(x^{2}-x\right)$ $\left(x^{2}-x+6\right)$ 7 (12) $x^{3}+x^{2}z+xz^{2}-y^{3}-y^{2}z-yz$ (2x2 5x) (2x2 $-5x+3\right)$ $+2$ (13) $x^{3}+3px^{2}+\left(3p^{2}-$ $q^{2}\right)x+p^{3}-p$ $\left(x^{2-x+1}\right)$ $\left(x^{2}-x+$ $-x+2\right)-12$ (14) $a^{2}\left(b-c\right)+$ b2 $\left(c-$ a) c $\left(a-b\right)$ (x2 $+5x+4\right)$ (x2 $+5x+6\right)-24$ (15) $ab\left(a-b\right)+$ $bc\left(b-c\right)+ca\left(c-a\right)$ $x\left(x+1\right)$ $\left(x+2\right)$ $\left(x+3\right)$ $-15$ (16) $a^{3}\left(b-c\right)+b$ $\left(c-a\right)+$ c $\left(a-$ b) $\left(x+1\right)$ $\left(x+2$ $113$ $\left(x+3\right)$ $3\right)\left(x$ $\left(x+4\right)$ $+\right)$ (17) $a^{4}+$ $c^{4}-2a$ $b^{2}-2b^{2}c^{2}-2c^{2}a$ $\left(x-1\right)\left($ $\left(x+2\right)$ $\right)\left(x-3\right)\left(x$ $\left(x+4\right)$ $+24$ (18) $a\left(b^{3}-c^{3}\right)+b\left(c^{3}-a^{3}\right)+$ $\left(a^{3}-b^{3}\right)$ $6\right)\left(x^{2}+7x+6\right)-3x^{2}$ (19) $+$ $-$ $a\right)^{3}+$ $\left(a\bar{7} $ b)3 $\left(x^{2}+5x+6\right)$ $\left(x+1\right)$ $\left(x+2\right)$ $\left(x+3\right)$ $3\right)\left(x+6\right)-8x$ (20) $\left(a+b\right)$ $c^{3}-\left(a^{2}+$ $ab+$ $b^{2}\right)c^{2}+$ a' b2 $1\right)\left(x+1\right)\left(y+1\right)$ $+xy$ $\left(xy+1$
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