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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise a...

Question

Factorise $a^{2} + b^{2} + 2 (a b + b c + c a)$

A

(a + b) (a + b + 2 c)

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B

(b + c) (c + a + 2 b)

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C

(c + a) (a + b + 2 c)

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D

(b + a) (b + c + 2 a)

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Solution

The correct option is A $(a + b) (a + b + 2 c)$
$a^{2} + b^{2} + 2 (a b + b c + c a)$
$= a^{2} + b^{2} + 2 a b + 2 (b c + c a)$
$= (a + b)^{2} + 2 c (a + b)$
$= (a + b) (a + b + 2 c)$

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Similar questions

Q. State True or False.

a^{2} + b^{2} - 2 (a b - a c + b c)

= (a - b) {(a - b) + 2 c} = (a - b) (a - b + 2 c)

Q. Prove the following identities:

\frac{2 a}{a + b} + \frac{2 b}{b + c} + \frac{2 c}{c + a} + \frac{(b - c) (c - a) (a - b)}{(b + c) (c + a) (a + b)} = 3

Q. If a,b and care non zero numbers, then

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} b^{2} c^{2} & b c & b + c c^{2} a^{2} & c a & c + a a^{2} b^{2} & a b & a + b \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} b + c & c + a & a + b c + a & a + b & b + c a + b & b + c & c + a \end{matrix} ∣ ∣ ∣ ∣ == 2 (a + b + c) (a b + b c + c a - a^{2} - b^{2} - c^{2})

Q. Prove the following identity:

\frac{a {(b - c)}^{2}}{(c - a) (a - b)} + \frac{b {(c - a)}^{2}}{(a - b) (b - c)} + \frac{c {(a - b)}^{2}}{(b - c) (c - a)} = a + b + c

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Standard IX Mathematics

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