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Factor Polynomials (Order 3) - Sum of Cubes (With Hint), Coefficient N

Level 1

This topic helps learners practice factoring third-order polynomials using the sum of cubes formula. The problems require recognizing the structure of sum and difference of cubes in the given polynomials and factoring them accordingly, with variables manipulated under different coefficients. Each example provides a specific polynomial and hints for simplifying the expressions using coefficients and variables to assist in solving the problems.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Factor Polynomials (Order 3) - Sum of Cubes (With Hint), Coefficient N Worksheet

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Factor Polynomials (Order 3) - Sum of Cubes (With Hint), Coefficient N
1
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 216n to the power of 3 - 216\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=6n
a A LaTex expression showing (6n + 36)(36n to the power of 2 + 36n + 6)
b A LaTex expression showing (6n - 6)(36n to the power of 2 + 36n - 36)
2
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 125p to the power of 3 - 64\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=5p
a A LaTex expression showing (5p - 4)(25p to the power of 2 + 20p - 16)
b A LaTex expression showing (5p + 125)(25p to the power of 2 - 20p + 16)
3
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 216w to the power of 3 + 27\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=6w
a A LaTex expression showing (3w - 3)(36w to the power of 2 + 18w - 9)
b A LaTex expression showing (6w + 3)(36w to the power of 2 - 18w + 9)
4
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 8z to the power of 3 - 216\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=2z
a A LaTex expression showing (2z - 6)(4z to the power of 2 + 12z - 36)
b A LaTex expression showing (2z + 6)(12z to the power of 2 - 4z + 36)
5
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 125w to the power of 3 + 64\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=5w
a A LaTex expression showing (5w + 4)(25w to the power of 2 - 20w + 16)
b A LaTex expression showing (4w + 25)(25w to the power of 2 - 20w + 16)
6
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 64z to the power of 3 - 27\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=4z
a A LaTex expression showing (4z + 3)(16z to the power of 2 - 12z + 9)
b A LaTex expression showing (4z - 3)(16z to the power of 2 + 12z - 9)
7
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 216w to the power of 3 - 216\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=6w
a A LaTex expression showing (6w + 36)(36w to the power of 2 - 36w + 36)
b A LaTex expression showing (6w - 6)(36w to the power of 2 + 36w - 36)
8
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 125n to the power of 3 - 125\\ \\ \text{hint:}\\a to the power of 3 + b to the power of 3 = (a + b)(a to the power of 2 - ab + b to the power of 2 )\\a=5n
a A LaTex expression showing (5n + 5)(25n to the power of 2 - 25n + 25)
b A LaTex expression showing (5n - 5)(25n to the power of 2 + 25n - 25)