Question
Simplify:$(a + b)^3 + (a - b)^3$
✓
Answer
$(a + b)^3 + (a - b)^3$
$= a^3 + b^3+ 3ab (a + b) + a^3 - 3ab (a - b) - b^3$
$= a^3+ b^3 + 3a^2b + 3ab^2 + a^3 - 3a^2b + 3ab^2 - b^3$
$= 2a^3+ 6ab^2.$
$= a^3 + b^3+ 3ab (a + b) + a^3 - 3ab (a - b) - b^3$
$= a^3+ b^3 + 3a^2b + 3ab^2 + a^3 - 3a^2b + 3ab^2 - b^3$
$= 2a^3+ 6ab^2.$
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
Factorise the following by taking out the common factors:$2x^5y + 8x^3y^2 - 12x^2y^3$
→The base of a right-angled triangle is 24 cm and its hypotenuse is 25 cm. Find the area of the triangle.
The mean of $4$ observations is $20.$ If one observation is excluded, the mean of the remaining observations becomes $15.$ Find the excluded observation.
→Express in terms of $\log 2$ and $\log 3$ : $\log 4.5$
→Evaluate :$\frac{3 \sin 3 B +2 \cos \left(2 B +5^{\circ}\right)}{2 \cos 3 B -\sin \left(2 B -10^{\circ}\right)}$; when $"B\ " = 20\circ.$
→Find the mean of daily wages of 60 workers in a factory as per data given below :
| Daily wages (in ₹) | 90 | 110 | 120 | 130 | 150 |
| No. of workers | 12 | 14 | 13 | 11 | 10 |
A number consists of two digits, the difference of whose digits is 3. If 4 times the number is equal to 7 times the number obtained by reversing the digits, find the number.
[Hint. Original number is greater than the number obtained by reversing its digits.
$\therefore$ In original number, ten's digit is greater than unit's digit.]
→[Hint. Original number is greater than the number obtained by reversing its digits.
$\therefore$ In original number, ten's digit is greater than unit's digit.]
In the given figure, $\text{PQR}$ is a triangle, in which $Q S \perp P R, Q S=3\ cm , P S=4\ cm$ and $Q R=12\ cm$, find the value of: $4 \sin ^2 R-\frac{1}{\tan ^2 P}$
→Draw the graph for the linear equation given below$:y = - x + 4$
→A copper wire when bent in the form of a square encloses an area of 272.25 $cm ^2$. If the same wire is bent into the form of a circle, what will be the area enclosed by the wire?
→