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Factorisation Using Algebraic Identities

Factorise the...

Question

Factorise the following expression: $25 m^{2} + 30 m + 9$ .

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Solution

Factorise the given expression by using properties:
We know that ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
Comparing this identity with $25 m^{2} + 30 m + 9$ , we get
${= (5 m)}^{2} + {(3)}^{2} + (5 m \times 3 \times 2) = {(5 m + 3)}^{2}$
Therefore, $25 m^{2} + 30 m + 9$ can be factorised as ${(5 m + 3)}^{2}$ .

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