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Mathematics

Factorise :

x2 + 6xy + 9y2 + x + 3y

Factorisation

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Answer

x2 + 6xy + 9y2 + x + 3y

Using the formula

[∵ (x + y)2 = x2 + y2 + 2xy]

= (x2 + 6xy + 9y2) + x + 3y

= ((x)2 + 2 ×\times x ×\times 3y + (3y)2) + x + 3y

= (x + 3y)2 + (x + 3y)

= (x + 3y)((x + 3y) + 1)

= (x + 3y)(x + 3y + 1)

Hence,x2 + 6xy + 9y2 + x + 3y = (x + 3y)(x + 3y + 1)

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