Factorise the following by grouping the terms:
l) $x y (a^{2} + 1) + a (x^{2} + y^{2})$

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Solution

Given: $x y (a^{2} + 1) + a (x^{2} + y^{2})$
$= a^{2} x y + x y + a x^{2} + a y^{2}$
On grouping the terms,
$= (a^{2} x y + a x^{2}) + (a y^{2} + x y)$
$= a x (a y + x) + y (a y + x)$
$= (a y + x) (a x + y)$
Hence, the answer is $(a y + x) (a x + y)$ .

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Factorisation Using Algebraic Identities

Standard VIII Mathematics

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Factorise the following by grouping the terms: l) xy(a2+1)+a(x2+y2)

Given: xy(a2+1)+a(x2+y2) =a2xy+xy+ax2+ay2 On grouping the terms, =(a2xy+ax2)+(ay2+xy) =ax(ay+x)+y(ay+x) =(ay+x)(ax+y) Hence, the answer is (ay+x)(ax+y).

Factorise the following by grouping the terms:
l) $x y (a^{2} + 1) + a (x^{2} + y^{2})$

Given: $x y (a^{2} + 1) + a (x^{2} + y^{2})$
$= a^{2} x y + x y + a x^{2} + a y^{2}$
On grouping the terms,
$= (a^{2} x y + a x^{2}) + (a y^{2} + x y)$
$= a x (a y + x) + y (a y + x)$
$= (a y + x) (a x + y)$
Hence, the answer is $(a y + x) (a x + y)$ .