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How do you factor #64v^3-125#?

Answer 1

Eva Abramson

#(4v-5)(16v^2+20v+25)#

This is a #color(blue)"difference of cubes"# and , in general, factorises as.

#color(red)(|bar(ul(color(white)(a/a)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(a/a)|)))........ (A)#

Now #64v^3=(4v)^3" and " 125=(5)^3#

#rArra=4v" and " b=5#

substitute into (A)

#rArr64v^3-125=(4v-5)(16v^2+20v+25)#

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Answer 2

Julia Adams

To factor 64v^3 - 125, you can use the difference of cubes formula, which states that a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a = 4v and b = 5. So, applying the formula, you get (4v - 5)(16v^2 + 20v + 25). Therefore, 64v^3 - 125 factors into (4v - 5)(16v^2 + 20v + 25).

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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.