$p (q^{2} + r^{2}) - q (r^{2} + p^{2})$ can be factorised as

(p + q) (r^{2} - p q)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(p - q) (r^{2} - p q)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(p - q) (p q - r^{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(p - q r) (p + q)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $(p - q) (r^{2} - p q)$
Given, $p (q^{2} + r^{2}) - q (r^{2} + p^{2})$
$= p q^{2} + p r^{2} - q r^{2} - p^{2} q$
$= q (p q - r^{2}) + p (r^{2} - p q)$
$= p (r^{2} - p q) - q (r^{2} - p q)$
$= (p - q) (r^{2} - p q)$

Suggest Corrections

Similar questions

[p^{2} + (q r)^{2}] [p^{2} - (q r)^{2}]

p = 1, q = 2, r = 3

△ P Q R

Q R^{2} = P Q^{2} + P R^{2}

∠ P

Δ P Q R

25^{\circ} a n d 65^{\circ}

\begin{matrix} (a) P Q^{2} + Q R^{2} = R P^{2} (b) P Q^{2} + R P^{2} = Q R^{2} (c) R P^{2} + Q R^{2} = P Q^{2} \end{matrix}

p = {log}_{2 a} a, q = {log}_{3 a} 2 a

r = {log}_{4 a} 3 a

q r (2 - p)

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ² + QR²= RP²

(ii) PQ² + RP²= QR²

(iii) RP² + QR²= PQ²

Join BYJU'S Learning Program