H Algebra 2/Trig · Unit 3
Name a and b, then use the cube formula. Factor out a common factor before you name the cubes.
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Difference of cubes
a³ − b³ = (a − b)(a² + ab + b²)
Sum of cubes
a³ + b³ = (a + b)(a² − ab + b²)
The middle sign is the opposite of the sign in the binomial.
One variable. The first term is x³.
a³ − b³ = (a − b)(a² + ab + b²)
a = x
b = 5
(x − 5)(x² + x×5 + 5²)
Square each part and multiply the middle term.
(x − 5)(x² + 5x + 25)
Answer: (x − 5)(x² + 5x + 25)
a³ − b³ = (a − b)(a² + ab + b²)
a = x
b = 4
(x − 4)(x² + x×4 + 4²)
Square each part and multiply the middle term.
(x − 4)(x² + 4x + 16)
Answer: (x − 4)(x² + 4x + 16)
a³ + b³ = (a + b)(a² − ab + b²)
a = x
b = 2
(x + 2)(x² − x×2 + 2²)
Square each part and multiply the middle term.
(x + 2)(x² − 2x + 4)
Answer: (x + 2)(x² − 2x + 4)
a³ − b³ = (a − b)(a² + ab + b²)
a = x
b = 6
(x − 6)(x² + x×6 + 6²)
Square each part and multiply the middle term.
(x − 6)(x² + 6x + 36)
Answer: (x − 6)(x² + 6x + 36)
a³ + b³ = (a + b)(a² − ab + b²)
a = x
b = 5
(x + 5)(x² − x×5 + 5²)
Square each part and multiply the middle term.
(x + 5)(x² − 5x + 25)
Answer: (x + 5)(x² − 5x + 25)
a³ + b³ = (a + b)(a² − ab + b²)
a = x
b = 4
(x + 4)(x² − x×4 + 4²)
Square each part and multiply the middle term.
(x + 4)(x² − 4x + 16)
Answer: (x + 4)(x² − 4x + 16)
Two variables.
a³ + b³ = (a + b)(a² − ab + b²)
a = x
b = 4y
(x + 4y)(x² − x(4y) + (4y)²)
Square each part and multiply the middle term.
(x + 4y)(x² − 4xy + 16y²)
Answer: (x + 4y)(x² − 4xy + 16y²)
a³ − b³ = (a − b)(a² + ab + b²)
a = x
b = 2y
(x − 2y)(x² + x(2y) + (2y)²)
Square each part and multiply the middle term.
(x − 2y)(x² + 2xy + 4y²)
Answer: (x − 2y)(x² + 2xy + 4y²)
a³ + b³ = (a + b)(a² − ab + b²)
a = 2x
b = 3y
(2x + 3y)((2x)² − (2x)(3y) + (3y)²)
Square each part and multiply the middle term.
(2x + 3y)(4x² − 6xy + 9y²)
Answer: (2x + 3y)(4x² − 6xy + 9y²)
a³ − b³ = (a − b)(a² + ab + b²)
a = 3x
b = y
(3x − y)((3x)² + (3x)y + y²)
Square each part and multiply the middle term.
(3x − y)(9x² + 3xy + y²)
Answer: (3x − y)(9x² + 3xy + y²)
a³ − b³ = (a − b)(a² + ab + b²)
a = 2x
b = y
(2x − y)((2x)² + (2x)y + y²)
Square each part and multiply the middle term.
(2x − y)(4x² + 2xy + y²)
Answer: (2x − y)(4x² + 2xy + y²)
a³ + b³ = (a + b)(a² − ab + b²)
a = 4x
b = 5y
(4x + 5y)((4x)² − (4x)(5y) + (5y)²)
Square each part and multiply the middle term.
(4x + 5y)(16x² − 20xy + 25y²)
Answer: (4x + 5y)(16x² − 20xy + 25y²)
Factor out the greatest common factor first.
Factor out the common factor 2.
2(27x³ − 1)
a³ − b³ = (a − b)(a² + ab + b²)
a = 3x
b = 1
(3x − 1)((3x)² + (3x)×1 + 1²)
Square each part and multiply the middle term.
(3x − 1)(9x² + 3x + 1)
2(3x − 1)(9x² + 3x + 1)
Answer: 2(3x − 1)(9x² + 3x + 1)
Factor out the common factor 2.
2(8x³ − 1)
a³ − b³ = (a − b)(a² + ab + b²)
a = 2x
b = 1
(2x − 1)((2x)² + (2x)×1 + 1²)
Square each part and multiply the middle term.
(2x − 1)(4x² + 2x + 1)
2(2x − 1)(4x² + 2x + 1)
Answer: 2(2x − 1)(4x² + 2x + 1)
Factor out the common factor 2.
2(27x³ + 8)
a³ + b³ = (a + b)(a² − ab + b²)
a = 3x
b = 2
(3x + 2)((3x)² − (3x)×2 + 2²)
Square each part and multiply the middle term.
(3x + 2)(9x² − 6x + 4)
2(3x + 2)(9x² − 6x + 4)
Answer: 2(3x + 2)(9x² − 6x + 4)
Factor out the common factor 3.
3(8x³ + 27y³)
a³ + b³ = (a + b)(a² − ab + b²)
a = 2x
b = 3y
(2x + 3y)((2x)² − (2x)(3y) + (3y)²)
Square each part and multiply the middle term.
(2x + 3y)(4x² − 6xy + 9y²)
3(2x + 3y)(4x² − 6xy + 9y²)
Answer: 3(2x + 3y)(4x² − 6xy + 9y²)
Factor out the common factor 3.
3(125x³ − 27)
a³ − b³ = (a − b)(a² + ab + b²)
a = 5x
b = 3
(5x − 3)((5x)² + (5x)×3 + 3²)
Square each part and multiply the middle term.
(5x − 3)(25x² + 15x + 9)
3(5x − 3)(25x² + 15x + 9)
Answer: 3(5x − 3)(25x² + 15x + 9)
Factor out the common factor 2.
2(x³ + 8)
a³ + b³ = (a + b)(a² − ab + b²)
a = x
b = 2
(x + 2)(x² − x×2 + 2²)
Square each part and multiply the middle term.
(x + 2)(x² − 2x + 4)
2(x + 2)(x² − 2x + 4)
Answer: 2(x + 2)(x² − 2x + 4)
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