What is factor 125(x+3)^3+(2y-1)^3 ?

The solution to factor 125(x+3)^3+(2y-1)^3 is (5x+2y+14)(25x^2+155x-10xy+4y^2+241-34y)

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factor 125(x+3)^3+(2y-1)^3

factor

125 (x + 3)^{3} + (2 y - 1)^{3}

(5 x + 2 y + 14) (25 x^{2} + 155 x - 10 x y + 4 y^{2} + 241 - 34 y)

Solution steps

125 (x + 3)^{3} + (2 y - 1)^{3}

Rewrite

125 (x + 3)^{3} + (2 y - 1)^{3}

(5 (x + 3))^{3} + (2 y - 1)^{3}

= (5 (x + 3))^{3} + (2 y - 1)^{3}

Apply Sum of Cubes Formula:

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

(5 (x + 3))^{3} + (2 y - 1)^{3} = (5 (x + 3) + (2 y - 1)) (5^{2} (x + 3)^{2} - 5 (x + 3) (2 y - 1) + (2 y - 1)^{2})

= (5 (x + 3) + (2 y - 1)) (5^{2} (x + 3)^{2} - 5 (x + 3) (2 y - 1) + (2 y - 1)^{2})

Refine

= (2 y + 5 (x + 3) - 1) ((2 y - 1)^{2} - 5 (x + 3) (2 y - 1) + 25 (x + 3)^{2})

Expand

5 (x + 3) + 2 y - 1 : 5 x + 2 y + 14

= (5 x + 2 y + 14) ((2 y - 1)^{2} - 5 (x + 3) (2 y - 1) + 25 (x + 3)^{2})

Expand

25 (x + 3)^{2} - 5 (x + 3) (2 y - 1) + (2 y - 1)^{2} : 25 x^{2} + 155 x - 10 x y + 4 y^{2} + 241 - 34 y

= (5 x + 2 y + 14) (25 x^{2} + 155 x - 10 x y + 4 y^{2} + 241 - 34 y)

x - x^{2}

2 7^{3} - 1728

x^{2 - 4 x}

4 x^{2} + 2 x y - 3 y + 3 x y

5 x^{3} + 1 0^{2} - 2 0^{2} - 40

What is factor 125(x+3)^3+(2y-1)^3 ?
The solution to factor 125(x+3)^3+(2y-1)^3 is (5x+2y+14)(25x^2+155x-10xy+4y^2+241-34y)