Question

expand the following :(3x + 7y)³​

Answer 1

We have been asked to expand $\sf{{(3x + 7y)}^{3}}$.

If we carefully observe the given problem ; it is in the form of the identity : $\sf{{(a+b)}^{3}}$. So we will use the same identity to solve the given problem.

Here we will take the values of a and b as :

$\sf{a = 3x}$

$\sf{b = 7y}$

Now we need to take a look at the whole formula :

$\sf{{(a+b)}^{3} = {(a)}^{3} + {(b)}^{3} +3{a}^{2}b + 3a{b}^{2} }$

Now simply we need to put up the values of a and b in their places :

$\small{\rightarrow{\sf{{(3x + 7y)} ^{3} = {(3x)}^{3} + {(7y)}^{3} + 3{(3x)}^{2} \times 7y + 3 \times 3x \times {(7y)}^{2} }}}$

$\small{\rightarrow{\sf{{(3x + 7y)} ^{3} = {27x}^{3}+ {343y}^{3} + 3 \times {9x}^{2} \times 7y + 3 \times 3x \times {(14y)}^{2} }}}$

$\small{\rightarrow{\sf{{(3x + 7y)} ^{3} = {27x}^{3}+ {343y}^{3} + 189{x}^{2}y+ 126x{y}^{2}}}}$