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How do you factor the trinomial #3x^2+21xy-54y^2#?

Answer 1

Eva Abramson

We have that

#3x^2+21xy-54y^2=3*(x^2+7xy-18y^2)=3*(x^2+9xy-2xy-18y^2)= 3*(x^2-2xy+9xy-18y^2)=3*(x(x-2y)+9y(x-2y))= 3*(x-2y)*(x+9y)#

Finally

#3x^2+21xy-54y^2=3*(x-2y)*(x+9y)#

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Answer 2

Eva Abramson

To factor the trinomial (3x^2 + 21xy - 54y^2), first factor out the greatest common factor, which is 3:

(3(x^2 + 7xy - 18y^2))

Next, factor the quadratic expression inside the parentheses:

(3(x + 9y)(x - 2y))

So, the factored form of (3x^2 + 21xy - 54y^2) is (3(x + 9y)(x - 2y)).

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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.