Factoring Difference of Cubes

Factoring Sum or Difference of Two Cubes

Factor completely different types of polynomials (sum and difference of two cubes, perfect square trinomials, and general trinomials). M8AL-Ia-b-1

Cube of a number

Find the cubes of the following.

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$$3^3$$  

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$$5^3$$  

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$$7^3$$  

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$$9^3$$  

Cube root of a number

Find the cube root of the following

note: use "^" for exponent (eg. x² = x^2)

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$$^3\sqrt{64}$$  

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$$^3\sqrt{125}$$  

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$$^3\sqrt{\frac{1}{27}}$$  

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$$^3\sqrt{x^3}$$  

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$$^3\sqrt{y^6}$$  

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$$^3\sqrt{216y^3}$$  

Simplify the following

note: use "^" for exponent (eg. x² = x^2)

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$$9^2$$  

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$$\left(3x\right)^2$$  

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$$\left(-5x\right)^2$$  

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$$2\left(-7x\right)\left(9y\right)$$  

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$$2\left(8x\right)\left(-3y\right)$$  

Open Ended

In figure A. What polynomial represents the volume of Figure A?

Volume = (a³ + _ )

Open Ended

In figure B. What polynomial represents the volume of Figure B?

Volume = (x³ - _ )

Open Ended

Suppose the square-boxes in Figure A has a total volume of a³ + 27 ft³, what is the value of b?

Open Ended

Suppose the volume of Figure B is x³ – 27 ft³, what is the value of y?

Open Ended

If the factored form of the (a³ + b³) is (a + b) (a² – ab + b²), what could be the factored form of a² + 27?

Open Ended

If the factored form of the (x³ + y³) is (x – y) (x² + xy + b²), what could be the factored form of x³ – 27?

WHAT'S MORE

Find the BINOMIAL FACTOR

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a³ + 1 = ___ (a² - a + 1)

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b³ + 8 = ___ (b² - 2b + 4)

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c³ - 1 = ___ (c² + c + 1)

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8f³ - 27 = ___ (4f² + 6f + 9)

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g³ + 343 = ___ (g² + 7g + 49)

WHAT'S MORE

Complete the factors with the missing term

note: use "^" for exponent (eg. x² = x^2)

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n³ + 27 = (n + 3)(n² - __ + 9)

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m³ + 729 = (m + 9)(m² - 9m + __)

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2x³ - 54 = 2(x - 3)(__ - 3x + 9)

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8x³ + 27y³ = (2x + 3y)(4x² - 6xy + __)

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x³ + 1000y³ = (x + 10y)(x² - ___ +100y²)