What is factor a^3b^3+8c^3 ?

The solution to factor a^3b^3+8c^3 is (ab+2c)(a^2b^2-2abc+4c^2)

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factor a^3b^3+8c^3

factor

a^{3} b^{3} + 8 c^{3}

(ab + 2 c) (a^{2} b^{2} - 2 ab c + 4 c^{2})

Solution steps

a^{3} b^{3} + 8 c^{3}

Rewrite

a^{3} b^{3}

(ab)^{3}

Rewrite

8 c^{3}

(2 c)^{3}

= (ab)^{3} + (2 c)^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(ab)^{3} + (2 c)^{3} = (ab + 2 c) ((ab)^{2} - ab 2 c + (2 c)^{2})

= (ab + 2 c) ((ab)^{2} - ab 2 c + (2 c)^{2})

Simplify

(ab + 2 c) ((ab)^{2} - ab \cdot 2 c + (2 c)^{2}) : (ab + 2 c) (a^{2} b^{2} - 2 ab c + 4 c^{2})

= (ab + 2 c) (a^{2} b^{2} - 2 ab c + 4 c^{2})

a d - b c - b d + a c

+ (- 2)

am + bm + a^{2} + ab

a x + a + b x + b

- (3)

What is factor a^3b^3+8c^3 ?
The solution to factor a^3b^3+8c^3 is (ab+2c)(a^2b^2-2abc+4c^2)