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Solving a Quadratic Equation by Factorization Method

Factorize : ...

Question

Factorize :
$(p^{2} - 2 p q + q^{2}) - r^{2}$

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Solution

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

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Q. Factorize the polynomial,

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

.

Factorize the following expressions

p^{2} + q^{2} + r^{2} + 2 p q + 2 q r + 2 r p

p^{2} - 2 p q + q^{2}

p^{2} + 2 p q - q^{2}

Q. Factorize each of the following algebraic expression:
25 − p² − q² − 2pq

p = x - y, q = y - z

r = z - r

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

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