Question
Factorize the following expressions: $2\sqrt{2}\text{a}^3+16\sqrt{2}\text{b}^3+\text{c}^3-12\text{abc}$
✓
Answer
$2\sqrt{2}\text{a}^3+16\sqrt{2}\text{b}^3+\text{c}^3-12\text{abc}$
$=\big(\sqrt{2}\text{a}\big)^3+\big(2\sqrt{2}\text{b}\big)^3+(\text{c})^3-3\times\sqrt{2}\text{a}\times2\sqrt{2}\text{b}\times\text{c}$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b})+\text{c}\big)\Big(\big(\sqrt{2}\text{a}\big)^2+\big(2\sqrt{2}\text{b})^2+\text{c}^2$
$\big(\sqrt{2}\text{a}\big)\big(2\sqrt{2}\text{b}\big)-\big(2\sqrt{2}\text{b}\big)\text{c}-\big(\sqrt{2}\text{a}\big)\text{c}\Big)$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2}\text{bc}-\sqrt{2}\text{ac}\big)$
$\therefore2\sqrt{2}\text{a}^3+16\sqrt{2}\text{b}^3+\text{c}^3-12\text{abc}$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2}\text{bc}-\sqrt{2}\text{ac}\big)$
$=\big(\sqrt{2}\text{a}\big)^3+\big(2\sqrt{2}\text{b}\big)^3+(\text{c})^3-3\times\sqrt{2}\text{a}\times2\sqrt{2}\text{b}\times\text{c}$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b})+\text{c}\big)\Big(\big(\sqrt{2}\text{a}\big)^2+\big(2\sqrt{2}\text{b})^2+\text{c}^2$
$\big(\sqrt{2}\text{a}\big)\big(2\sqrt{2}\text{b}\big)-\big(2\sqrt{2}\text{b}\big)\text{c}-\big(\sqrt{2}\text{a}\big)\text{c}\Big)$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2}\text{bc}-\sqrt{2}\text{ac}\big)$
$\therefore2\sqrt{2}\text{a}^3+16\sqrt{2}\text{b}^3+\text{c}^3-12\text{abc}$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2}\text{bc}-\sqrt{2}\text{ac}\big)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the mean of first five multiples of $3$
→How many irrational numbers lie between $\sqrt{2}$ and $\sqrt{3}?$ Find any three irrational numbers lying between $\sqrt{2}$ and $\sqrt{3}.$
→If the volume of a right circular cone of height $9 \ cm$ is $48 \pi \ cm^3$, find the diameter of its base.
→Factorise: $\text{x}^2-\sqrt{3}\text{x}-6$
→ Examine whether the following number are rational or irrational: $\sqrt{8}+4\sqrt{32}-6\sqrt{2}$
→Write four solutions of the equation: $2x + y = 7$
→Prove the exterior angle formed by producing a side of a cyclic quadrilateral is equal to the interior opposite angle.
$A B C D$ is a quadrilateral in which $A D=B C$ and $\angle D A B=\angle C B A$ : Prove that:
i. $\triangle A B D \cong \triangle B A C$
ii. $B D=A C$
iii. $\angle ABD =\angle BAC$
→i. $\triangle A B D \cong \triangle B A C$
ii. $B D=A C$
iii. $\angle ABD =\angle BAC$
Multiply:
$\left(x^2+y^2+z^2-x y+x z+y z\right) b y(x+y-z)$
→$\left(x^2+y^2+z^2-x y+x z+y z\right) b y(x+y-z)$
Factorise: $\text{x}^2+\sqrt{2}\text{x}-24$
→