Question

Simplify the following using suitable identities (3p+8q)^2 + (3p-8q)^2 - (s+4) (s-5)​

Answer 1

Step-by-step explanation:

${\red{\underline{\underline{\bold{Given:-}}}}}$

• $\sf {(3p + 8q)}^{2} + {(3p - 8q)}^{2} - (s + 4)(s - 5)$

${\blue{\underline{\underline{\bold{Solution:-}}}}}$

$\sf \: By \: \: using \: \: the \: \: identity:-$

$\sf \green{(a \: + \: b)(a \: - \: b) = {a}^{2} - {b}^{2} }$

$\sf {(3p + 8q)}^{2} + {(3p - 8q)}^{2} - (s + 4)(s - 5)$

$\sf {(3p )}^{2} - {( 8q)}^{2} - (s + 4)(s - 5)$

$\sf {9p}^{2} - {64q}^{2} - \big \{s(s - 5) + 4(s - 5) \big \}$

$\sf {9p}^{2} - {64q}^{2} - \big \{ ( {s}^{2} - 5s) + (4s - 20) \big \}$

$\sf {9p}^{2} - {64q}^{2} - \big \{ {s}^{2} - 5s + 4s - 20 \big \}$

$\sf {9p}^{2} - {64q}^{2} - \big \{ {s}^{2} - s - 20 \big \}$

$\boxed{ \sf \purple{{9p}^{2} - {64q}^{2} - {s}^{2} + s + 20}}$