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

The solution to factor 125(x+3)^3+(2y+1)^3 is (5x+2y+16)(25x^2+145x-10xy+4y^2+211-26y)

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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 + 16) (25 x^{2} + 145 x - 10 x y + 4 y^{2} + 211 - 26 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 + 16

= (5 x + 2 y + 16) ((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} + 145 x - 10 x y + 4 y^{2} + 211 - 26 y

= (5 x + 2 y + 16) (25 x^{2} + 145 x - 10 x y + 4 y^{2} + 211 - 26 y)

- 8 x - 25 + \frac{25}{4}

9 x^{3} - 3 x^{3}

- 8 e^{t} x - e^{t} y

x x^{2} + 2 x - 8

- 1 (- 4 + m)

What is factor 125(x+3)^3+(2y+1)^3 ?
The solution to factor 125(x+3)^3+(2y+1)^3 is (5x+2y+16)(25x^2+145x-10xy+4y^2+211-26y)