The sum of two binomials is (5x - 6xy + 7y - 30). If one of the binomial is (3xy - 2x + y), what is the other binomial?

(7x + 9xy + 6y - 30)

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(3x - 9xy + 6y - 30)

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(7x - 9xy - 6y - 30)

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(3x - 9xy + 6y - 30)

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Solution

The correct option is B (3x - 9xy + 6y - 30)
Let 's' be the term to be added to (3xy - 2x + y) to get (5x - 6xy + 7y - 30).
$\Rightarrow (3 x y - 2 x + y) + s = (5 x - 6 x y + 7 y - 30)$
$\Rightarrow s = (5 x - 6 x y + 7 y - 30) - (3 x y - 2 x + y)$
Grouping the like terms together, we get
$\Rightarrow s = (5 x + 2 x) + (- 6 x y - 3 x y) + (7 y - y) - 30$
$\Rightarrow s = 7 x - 9 x y + 6 y - 30$
So, the second binomial term is (7x - 9xy + 6y - 30).

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