Factoring Sum or Difference of Two 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)