Question
Factorise:$2\sqrt{2}\text{a}^3+16\sqrt{2}\text{b}^3+\text{c}^3-12\text{abc}$
✓
Answer
$x =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\big(\sqrt{2}\text{a}\big)\times\big(2\sqrt{2}\text{b}\big)\times(\text{c})$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\Big[\big(\sqrt{2}\text{a}\big)^2+(2\sqrt{2}\text{b})^2+\text{c}^2\\-\big(\sqrt{2}\text{a}\big)\times\big(2\sqrt{2}\text{b}\big)-\big(2\sqrt{2}\text{b}\big)\times(\text{c})-\big(\sqrt{2}\text{a}\big)\times(\text{c})\Big]$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2\text{bc}}-\sqrt{2}\text{ac}\big)$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\Big[\big(\sqrt{2}\text{a}\big)^2+(2\sqrt{2}\text{b})^2+\text{c}^2\\-\big(\sqrt{2}\text{a}\big)\times\big(2\sqrt{2}\text{b}\big)-\big(2\sqrt{2}\text{b}\big)\times(\text{c})-\big(\sqrt{2}\text{a}\big)\times(\text{c})\Big]$
$=\big(\sqrt{2}\text{a}+2\sqrt{2}\text{b}+\text{c}\big)\big(2\text{a}^2+8\text{b}^2+\text{c}^2-4\text{ab}-2\sqrt{2\text{bc}}-\sqrt{2}\text{ac}\big)$
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
Show that:$\frac{\Big(\text{a}+\frac{1}{\text{b}}\Big)^\text{m}\times\Big(\text{a}-\frac{1}{\text{b}}\Big)^\text{n}}{\Big(\text{b}+\frac{1}{\text{a}}\Big)^\text{m}\times\Big(\text{b}-\frac{1}{\text{a}}\Big)^\text{n}}=\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m}+\text{n}}$
→Factorise:
$x^2-32 x-105$
→$x^2-32 x-105$
Find the following products:$\Big(\frac{2}{\text{x}}+3\text{x}\Big)\Big(\frac{4}{\text{x}^2}+9\text{x}^2-6\Big)$
→Find the product.
$(x + y - z)(x^2 + y^2 + z^2 - xy + yz + zx)$
→$(x + y - z)(x^2 + y^2 + z^2 - xy + yz + zx)$
Curved surface area of a cylinder is $1980 cm ^2$ and radius of its base is $15 cm$. Find the height of the cylinder. $\left(\pi=\frac{22}{7}\right)$
Given: Curved surface area of cylinder $=1980$ sq.cm., radius $(r)=15 cm$
To find: Height of the cylinder (h)
→Given: Curved surface area of cylinder $=1980$ sq.cm., radius $(r)=15 cm$
To find: Height of the cylinder (h)
Factorise:
$16 x^4-1$
→$16 x^4-1$
Factorise:
$2 x^2+11 x-21$
→$2 x^2+11 x-21$
Draw a parallelogram PQRS. Draw diagonals PR and QS. Denote the intersection of diagonals by letter O. Compare the two parts of each diagonal with a divider. What do you find?
Factorise:
$a^3-0.064$
→$a^3-0.064$
Find the value of $x$ in the following:
$5^{x-3} \times 3^{2 x-8}=225$
→$5^{x-3} \times 3^{2 x-8}=225$