Home > Algebra > Factor Polynomials Using Special Products

How do you factor # 27y^3+64#?

Answer 1

Kennedy Adams

#27y^3+64=(3y+4)(9y^2-12y+16)#

Note that both #27y^3 = (3y)^3# and #64=4^3# are perfect cubes.

So it is natural to use the sum of cubes identity:

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

with #a=3y# and #b=4# as follows:

#27y^3+64#

#=(3y)^3+4^3#

#=(3y+4)((3y)^2-(3y)(4)+4^2)#

#=(3y+4)(9y^2-12y+16)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jameson Allen

To factor the expression 27y^3 + 64, you can use the sum of cubes formula, which states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). Applying this formula, where a = 3y and b = 4:

27y^3 + 64 = (3y)^3 + 4^3 = (3y + 4)(9y^2 - 12y + 16).

By signing up, you agree to our Terms of Service and Privacy Policy

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.