How do you factor 100+4x2−16y−40x?

1 Answer
George C.
Apr 21, 2017

If the −16y should have been −16y2, then we find:

100+4x2−16y2−40x=4(x−2y−5)(x+2y−5)

Explanation:

For the record: I think the question should have specified −16y2 rather than −16y. Here's what happens if that is the case:

The difference of squares identity can be written:

a2−b2=(a−b)(a+b)

Use this with a=(x−5) and b=2y as follows:

100+4x2−16y2−40x=4(x2−10x+25−4y2)

100+4x2−16y2−40x=4(x2−2x(5)+52−4y2)

100+4x2−16y2−40x=4((x−5)2−(2y)2)

100+4x2−16y2−40x=4((x−5)−2y)((x−5)+2y)

100+4x2−16y2−40x=4(x−2y−5)(x+2y−5)

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