Match the following expressions using suitable identities.

(m - 4)^{2}

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(m + 2) (m + 7)

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(3 m + 2) (3 m - 2)

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Solution

(i) $m^{2} + 9 m + 14$
Comparing above expression with the identity $x^{2} + (a + b) x + a b$
we note that $a b = 14 and (a + b) = 9.$
$S i n c e, (7 + 2) = 9 a n d (7) (2) = 14$
Hence,
$m^{2} + 9 m + 14$
= $m^{2} + 7 m + 2 m + 14$
= $m (m + 7) + 2 (m + 7)$
= $(m + 2) (m + 7)$

(ii) $9 m^{2} - 4$
Above expression can be written as,
$= (3 m)^{2} - (2)^{2}$
Using the identity: $a^{2} - b^{2} = (a + b) (a - b)$
$\Rightarrow 9 m^{2} - 4 = (3 m + 2) (3 m - 2)$

(iii) $m^{2} - 8 m + 16$
$= m^{2} - 2 \times m \times 4 + (4)^{2}$
Using the identity: $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$\Rightarrow m^{2} - 8 m + 16 = (m - 4)^{2}$

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