Lutasin ang {l}{(a-2b)^{2}(a+2b)^{3}-(a^{3}-8b^{3})(a^{3}+8b^{3})-12a^{2}b^{2}(2b+a)(-a+2b)}{(x^{2}+x+1)(x^2+x-1)-(x^2-1)^2-3(x-1)(x+1)-2^0}

$$\left. \begin{array} { l } { ( a - 2 b ) ^ { 2 } ( a + 2 b ) ^ { 3 } - ( a ^ { 3 } - 8 b ^ { 3 } ) ( a ^ { 3 } + 8 b ^ { 3 } ) - 12 a ^ { 2 } b ^ { 2 } ( 2 b + a ) ( - a + 2 b ) } \\ { ( x ^ { 2 } + x + 1 ) ( x ^ { 2 } + x - 1 ) - ( x ^ { 2 } - 1 ) ^ { 2 } - 3 ( x - 1 ) ( x + 1 ) - 2 ^ { 0 } } \end{array} \right.$$

Least Common Multiple

$$-2\left(a-2b-1\right)\left(a-2b\right)^{2}\left(x\left(a+2b\right)\right)^{3}$$

Mga Hakbang ng Solution

I-factor ang mga expression na hindi pa na-factor.

$$\left(a+2b\right)^{3}\left(a-2b\right)^{2}-\left(a-2b\right)^{2}\left(a+2b\right)^{3}a+2\left(a-2b\right)^{2}\left(a+2b\right)^{3}b=\left(-a+2b+1\right)\left(a-2b\right)^{2}\left(a+2b\right)^{3}$$

Tukuyin ang lahat ng factor at ang highest power ng mga ito sa lahat ng expression. I-multiply ang mga highest power ng mga factor na ito para makuha ang least common multiple.

$$-2\left(a-2b-1\right)\left(a+2b\right)x^{3}\left(a^{2}-4b^{2}\right)^{2}$$

Palawakin ang expression.

$$24b^{2}x^{3}a^{4}-96a^{2}x^{3}b^{4}+128x^{3}b^{6}-2x^{3}a^{6}+4bx^{3}a^{4}+32ax^{3}b^{4}-32a^{2}b^{3}x^{3}-16b^{2}a^{3}x^{3}+2x^{3}a^{5}+64x^{3}b^{5}$$

I-evaluate

$$\left(2b-a+1\right)\left(a-2b\right)^{2}\left(a+2b\right)^{3},\ 2x^{3}$$