Question
Factorize the following expressions:
$a^{12}+b^{12}$
$a^{12}+b^{12}$
✓
Answer
$=\left(a^4\right)^3+\left(b^4\right)^3$
$=\left(a^4+b^4\right)\left(\left(a^4\right)^2-a^4 \times b^4+\left(b^4\right)^2\right)\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=\left(a^4+b^4\right)\left(a^8-a^4 b^4+b^8\right)$
$\therefore a^{12}+b^{12}=\left(a^4+b^4\right)\left(a^8-a^4 b^4+b^8\right)$
$=\left(a^4+b^4\right)\left(\left(a^4\right)^2-a^4 \times b^4+\left(b^4\right)^2\right)\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]$
$=\left(a^4+b^4\right)\left(a^8-a^4 b^4+b^8\right)$
$\therefore a^{12}+b^{12}=\left(a^4+b^4\right)\left(a^8-a^4 b^4+b^8\right)$
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
An angle is equal to 8 times its complement. Determine its measure.
In the given figure, side BC of $\triangle\text{ABC}$ is produced to D. If $\angle\text{ACD}=128^\circ$ and $\angle\text{ABC}=43^\circ,$ find $\angle\text{BAC}$ and $\angle\text{ACB}.$
→Look at several examples of rational numbers in the form $\frac{\text{p}}{\text{q}}(\text{q}\neq0),$ where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?
→Factorise:
$1029-3 x^3$
→$1029-3 x^3$
Compute the value of x in the following figures.
The mean of marks scored by 100 students was found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Find the correct mean.
If the supplement of an angle is three times its complement, find the angle.
When one pair of corresponding angles is congruent, then all the remaining pairs of corresponding angles are congruent.
Factorise:
$x^2-26 x+133$
→$x^2-26 x+133$
Check the following are the solution of the equation 5x - 4y = 20.
(0, 5)
(0, 5)