Factorise:
$49 y^{2} + 84 y z + 36 z^{2}$

(7 y + 6 z)^{2}

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(y + 6 z)^{2}

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(y - 6 z)^{2}

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(7 y - 6 z)^{2}

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Solution

The correct option is A $(7 y + 6 z)^{2}$
Given expression is $49 y^{2} + 84 y z + 36 z^{2}$
$= (7 y)^{2} + 2 \times 7 y \times 6 z + (6 z)^{2}$
It is in the form of $a^{2} + 2 a b + b^{2} = (a + b)^{2}$
Substitute $a = 7 y, b = 6 z$
$\Rightarrow (7 y)^{2} + 2 \times 7 y \times 6 z + (6 z)^{2} = (7 y + 6 z)^{2}$
Therefore, the factors of the given expression are $(7 y + 6 z)^{2}$

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