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How do you factor # 64x^4 + xy^3#?

Answer 1

Kennedy Adams

#64x^4+xy^3 = x(4x+y)(16x^2-4xy+y^2)#

The sum of cubes identity can be written:

#a^3+b^3 = (a+b)(a^2-ab+b^2)#

Use this with #a=4x# and #b=y# as follows:

#64x^4+xy^3 = x(64x^3+y^3)#

#color(white)(64x^4+xy^3) = x((4x)^3+y^3)#

#color(white)(64x^4+xy^3) = x(4x+y)((4x)^2-(4x)y+y^2)#

#color(white)(64x^4+xy^3) = x(4x+y)(16x^2-4xy+y^2)#

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Answer 2

Isaiah Anthony

To factor (64x^4 + xy^3), you can factor out the greatest common factor, which is (x).

So, (64x^4 + xy^3 = x(64x^3 + y^3)).

Now, we have the sum of cubes in the parentheses, which can be factored using the formula (a^3 + b^3 = (a + b)(a^2 - ab + b^2)).

Applying this formula, we get:

(64x^3 + y^3 = (4x)^3 + (y)^3).

So, the factored form of (64x^4 + xy^3) is (x(4x + y)(16x^2 - 4xy + y^2)).

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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.