How do you factor #y^2+2xy - 63x^2 #?

Answer 1

Notice that #63 = 9 xx 7# and #2 = 9 - 7#, so

#y^2+2xy-63x^2 = (y-7x)(y+9x)#

When the coefficient of the first term in one of these quadratics is #1#, look for factors of the coefficient of the last term, whose sum or difference is the middle coefficient.

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Answer 2

Isaiah Anthony

To factor the expression ( y^2 + 2xy - 63x^2 ), we look for two numbers that multiply to give ( -63 ) and add to give ( 2 ). These numbers are ( 9 ) and ( -7 ). Therefore, we rewrite the middle term as ( 9xy - 7xy ). Now, we can factor by grouping:

[ y^2 + 9xy - 7xy - 63x^2 ]

[ = y(y + 9x) - 7x(y + 9x) ]

[ = (y - 7x)(y + 9x) ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.