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Multiplication of a Binomial by a Monomial

Subtract 3k...

Question

Subtract $3 k (5 k - l - 3 m)$ from $6 k (2 k + 3 l - 2 m)$

A

- 3 k^{2} + 21 k l - 3 k m

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B

- 4 k^{2} + 21 k l - 3 k m

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C

- 3 k^{2} - 21 k l - 3 k m

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D

None of these

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Solution

The correct option is A $- 3 k^{2} + 21 k l - 3 k m$
We find the subtraction of the given polynomials $3 k (5 k - l - 3 m), 6 k (2 k + 3 l - 2 m)$ by combining the like terms as shown below:

$6 k (2 k + 3 l - 2 m) - 3 k (5 k - l - 3 m) = 12 k^{2} + 18 k l - 12 k m - 15 k^{2} + 3 k l + 9 k m = (12 k^{2} - 15 k^{2}) + (18 k l + 3 k l) + (- 12 k m + 9 k m) = k^{2} (12 - 15) + k l (18 + 3) + k m (- 12 + 9) = - 3 k^{2} + 21 k l - 3 k m$

Hence, $6 k (2 k + 3 l - 2 m) - 3 k (5 k - l - 3 m) = - 3 k^{2} + 21 k l - 3 k m$ .

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