Question

Find the value of : (4pq + 3q)^2 – (4pq – 3q)^2​

Answer 1

Answer:

= (4pq+3q+4pq-3q)[4pq+3q - (4pq-3q)]

= 8pq (4pq+3q - 4pq+3q)

= 8pq×6q

= 8pq×6q=48pq^2

step explanation:

Answer 2

Question :

Find the Value of :

• (4pq + 3q)² - (4pq - 3q)²

To Find :

The Value of the Expression :

We Know :

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

Solution :

$\purple{\bf{\underline{(4pq + 3q)^{2} - (4pq - 3q)^{2}}}}$

By using the two identities , we get :

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}\\{(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

$\implies \rm{(4pq)^{2} + 2 \times 4pq \times 3q + (3q)^{2} - \big((4pq)^{2} - 2 \times 4pq \times 3q + (3q)^{2}\big)} \\ \\ \\ \implies \rm{16p^{2}q^{2} + 24pq^{2} + 9q^{2} - \big(16p^{2}q^{2} - 24pq^{2} + 9q^{2}\big)} \\ \\ \\ \implies \rm{16p^{2}q^{2} + 24pq^{2} + 9q^{2} - 16p^{2}q^{2} + 24pq^{2} - 9q^{2}} \\ \\ \\ \implies \rm{24pq^{2} + 9q^{2} + 24pq^{2} - 9q^{2}} \\ \\ \\ \implies \rm{24pq^{2} + 24pq^{2}} \\ \\ \\ \implies \rm{48pq^{2}} \\ \\ \\ \therefore \purple{\rm{48pq^{2}}}$

Hence , the value of (4pq + 3q)² - (4pq - 3q)² is 48pq².

Alternative Method :

We Know that ,

(a + b)² - (a - b)² = 4ab

By using this identity in the Equation , we get :

$\purple{\bf{\underline{(4pq + 3q)^{2} - (4pq - 3q)^{2}}}} \\ \\ \\ \implies \rm{(4pq + 3q)^{2} - (4pq - 3q)^{2} = 4 \times 4pq \times 3q} \\ \\ \\ \implies \rm{(4pq + 3q)^{2} - (4pq - 3q)^{2} = 48pq^{2}} \\ \\ \\ \therefore \purple{\rm{(4pq + 3q)^{2} - (4pq - 3q)^{2} = 48pq^{2}}}$

Hence , the value of (4pq + 3q)² - (4pq - 3q)² is 48pq².