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Multiplication of Three or More Monomials

Question 12Pr...

Question

Question 12

Product of $6 a^{2} - 7 b + 5 a b$ and $2 a b$ is
a) $12 a^{3} b - 14 a b^{2} + 10 a b$
b) $12 a^{3} b - 14 a b^{2} + 10 a^{2} b^{2}$
c) $6 a^{2} - 7 b + 7 a b$
d) $12 a^{2} b - 7 a b^{2} + 10 a b$

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Solution

b) $12 a^{3} b - 14 a b^{2} + 10 a^{2} b^{2}$
$\to$ Required product = $2 a b \times (6 a^{2} - 7 b + 5 a b)$
This is product of a trinomial by a monomial, so we multiply monomial with each term of the trinomial.
$∴ 2 a b \times (6 a^{2} - 7 b + 5 a b) = 2 a b \times 6 a^{2} + 2 a b \times (- 7 b) + 2 a b \times 5 a b = 12 a^{3} b - 14 a b^{2} + 10 a^{2} b^{2}$

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