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Question

Find the following product and verify the result for x = − 1, y = − 2:
13x-y2513x+y25

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Solution

To multiply, we will use distributive law as follows:

13x-y2513x+y25=13x13x+y25-y2513x+y25=19x2+xy215-xy215+y425=19x2+xy215-xy215-y425=19x2-y425

13x-y2513x+y25=19x2-y425

Now, we will put x = -1 and y = -2 on both the sides to verify the result.

LHS = 13x-y2513x+y25=13-1--22513-1+-225=-13-45-13+45=-1715715=-119225

RHS=19x2-y425=19-12--2425=19×1-1625=19-1625=-119225

Because LHS is equal to RHS, the result is verified.

Thus, the answer is 19x2-y425.

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