How do you factor #42x^2 + 5xy - 25y^2#?

Answer 1

#(6x-5)(7x+5)#

#(6x-5)(7x+5)#

You can use the quadratic formula or the cross-multiply rule (i think that's what it's called)

Quadratic formula = #(-b+-sqrt(b^2-4ac))/(2a)#
#a=42,b=5,c=-25#
#x=(-5+-sqrt(5^2-4*42*-25))/(2*42)#
#x=(-5+-sqrt(4225))/84#
#x=(-5+-65)/84#
#x=-70/84=-5/6# or #x=60/84=5/7#

So your equation is

#(x-5/6)(x+5/7)#
=#(6x-5)(7x+5)#
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Answer 2

To factor the expression 42x^2 + 5xy - 25y^2, you can use the method of factoring by grouping. First, find two numbers that multiply to give you 42 times -25, which is -105, and add up to 5. The numbers are 15 and -7. Then, rewrite the middle term using these numbers as coefficients: 5xy = 15xy - 7xy. Now, group the terms: (42x^2 + 15xy) - (7xy + 25y^2). Factor out the greatest common factor from each group: 3x(14x + 5y) - 5y(7x + 5y). Finally, factor out the common binomial factor: (3x - 5y)(14x + 5y).

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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.

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.

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.

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.

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