Question

Do as directed :
Using suitable identity and find

1) (4p-3q)^2
​

Answer 1

Question :-

Using Suitable Identity, Find : $\mathrm {(4p-3q)^2}$

$\begin {gathered} \end {gathered}$

Solution :-

Putting 4p = x and 3q = y, we get -

$\begin {aligned} \bold {(4p-3q)^2} &\Rightarrow \boxed {\mathtt {(x-y)^2} = \mathtt {x^2 - 2xy + y^2}}\\\\&\Rightarrow (4p)^2 - 2 \times 4p \times 3q + (3q)^2\\\\&= \bf 16p^2 - 24pq + 9q^2 \end {aligned}$

∴ $\boxed {\bf (4p - 3q)^2 = 16p^2 - 24pq + 9q^2}$

$\begin {gathered} \end {gathered}$

Additional Information :-

Some more Formulae for Factorization :-

i. $\mathtt{(x + y)^2 = x^2 + 2xy + y^2}$

ii. $\mathtt{x^2 - y^2 = (x+ y)(x - y)}$

iii. $\mathtt{(x + a)(x + b) = x^2 + (a +b) x + ab}$

iv. $\mathtt {(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2xz}$

v. $\mathtt {(x + y)^3 = x^3 + y^3 + 3xy (x+y)}$

vi. $\mathtt {(x - y)^3 = x^3 - y^3 - 3xy (x - y)}$

vii. $\mathtt{x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - xz)}$