Reduce the following expression using binomial identities: $(3 x + 5) (3 x + 10)$ .

9 x^{2} + 45 x + 50

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9 x^{2} - 45 x + 50

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9 x^{2} + 45 x - 50

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9 x^{2} + 45 - 50

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Solution

The correct option is A $9 x^{2} + 45 x + 50$
We know that binomial identities for $(x + y) (x + z) = x^{2} + (y + z) x + y z$
So, $x = 3 x, y = 5, z = 10$
$=$ $(3 x)^{2} + (5 + 10) 3 x + 5 \times 10$
$=$ $9 x^{2} + 45 x + 50$

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