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Factorisation by Regrouping Terms

Factorize eac...

Question

Factorize each of the following expressions:
qr − pr + qs − ps

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Solution

$q r - p r + q s - p s = (q r - p r) + (q s - p s) [G r o u p i n g t h e e x p r e s s i o n s] = r (q - p) + s (q - p) = (r + s) (q - p) [T a k i n g (q - p) a s t h e c o m m o n f a c t o r]$

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¯ ¯¯¯¯¯¯ ¯ R T

¯ ¯¯¯¯¯¯ ¯ P S

¯ ¯¯¯¯¯¯ ¯ Q S

¯ ¯¯¯¯¯¯ ¯ P R

¯ ¯¯¯¯¯¯ ¯ P S

Δ P Q R, ∠ P Q R = 90^{o}

Q S ⊥

P R

P S = 4

S R = 9

Q S

⊥

=

∠

= 40^{o}

∠

= 20^{o}

In triangle PQR ,PS id the busectorbof angleQPR.show that

QS/SR = PQ/PR.

∠ S P Q = ∠ R Q P

∠ Q P R = ∠ P Q S

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