Solve: 16-a^6+4 a^3 b^3-4 b^6 - Vidyadip

Question

Solve:
$16-a^6+4 a^3 b^3-4 b^6$

✓

Answer

$16-a^6+4 a^3 b^3-4 b^6$
$=16-\left(a^6-4 a^3 b^3+4 b^6\right)$
$=4^2-\left[\left(a^3\right)^2-2 \times a^3 \times 2 b^3+\left(2 b^3\right)^2\right]$
$=4^2-\left(a^3-2 b^3\right)^2$
$=\left[4-\left(a^3-2 b^3\right)\right]\left[4+\left(a^3-2 b^3\right)\right]$
$\left.=\left(4-a^3-2 b^3\right)\left(4+a^3-2 b^3\right)\right]$
$=\left(a^3-2 b^3+4\right)\left(-a^3-2 b^3+4\right)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Mark Question" from Factorization→Factorization — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

If 18 dolls cost Rs. 630, how many dolls can be bought for Rs. 455?

Ramesh deposited Rs, 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months.

Verify the property: x × (y + z) = x × y + x × z by taking:
$\text{x}=\frac{-12}{5},\text{y}=\frac{-15}{4},\text{z}=\frac{8}{3}$

Multiply the monomial by the binomial and find the value of $x=-1, y=0.25$ and $z=0.05$ :
$z^2(x-y)$

Using commutativity and associativity of addition of rational numbers, express the following as a rational number:
$\frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3}$

$9.8 \times 10.2$

By what number should $(-6)^{-1}$ be multiplied so that the product becomes $9^{-1}$ ?

Twenty-one cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m , what will be the cost of cleaning them at the rate of Rs 2.50per square meter?

Find the volume of a cylinder, the diameter of whose base is 7cm and height being 60cm. Also, find the capacity of the cylinder in litres.

Expand : $\left(2 m+\frac{1}{5}\right)^3$