Lutasin ang {l}{3(x+2)^2-6}{(x+5)^2-24}

$$\left. \begin{array} { l } { 3 ( x + 2 ) ^ { 2 } - 6 } \\ { ( x + 5 ) ^ { 2 } - 24 } \end{array} \right.$$

Least Common Multiple

$$3\left(\left(x+2\right)^{2}-2\right)\left(\left(x+5\right)^{2}-24\right)$$

Mga Hakbang ng Solution

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

$$3\left(x+2\right)^{2}-6=3\left(x-\left(\sqrt{2}-2\right)\right)\left(x-\left(-\sqrt{2}-2\right)\right) \left(x+5\right)^{2}-24=\left(x-\left(-2\sqrt{6}-5\right)\right)\left(x-\left(2\sqrt{6}-5\right)\right)$$

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.

$$3\left(x-\left(-\sqrt{2}-2\right)\right)\left(x-\left(-2\sqrt{6}-5\right)\right)\left(x-\left(\sqrt{2}-2\right)\right)\left(x-\left(2\sqrt{6}-5\right)\right)$$

Palawakin ang expression.

$$3x^{4}+42x^{3}+129x^{2}+72x+6$$

I-evaluate

$$3\left(\left(x+2\right)^{2}-2\right),\ \left(x+5\right)^{2}-24$$