Factoring Polynomials: Sum and Difference of Cubes Answers

Hank’s teacher asked him to verify that the product (y−3)(y2+3y+9) is a difference of cubes. He used the distributive property to multiply the binomial times the trinomial. Before simplifying, his product was a polynomial of the form y3+3y2+ay−3y2−ay−27. What is the value of a in the polynomial?

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?

Which is the factorization of x3 + 8?

What is 125x9 + 64y12 written as a sum of cubes?

What is the cube root of 27x18?

Which product will result in a sum or difference of cubes?

Which monomial is a perfect cube?

Which statements are true about a perfect cube monomial and its roots? Check all that apply.A perfect cube monomial must have exponents on the variables.A perfect cube monomial must have three identical roots, such that the product of the roots equal the perfect square monomial.The coefficient of the monomial must be divisible by 3.Any monomial can be a perfect cube root.The least common multiple of all the exponents on variables of a perfect cube monomial must be 3.It must be possible for the coefficient of a perfect cube monomial to be written in the form n3, where n equals the cube root of the coefficient.

Which expression is equivalent to ?

The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k?