What is factor (a+b)^3-(2a+3b)^3 ?

The solution to factor (a+b)^3-(2a+3b)^3 is (-a-2b)(7a^2+19ab+13b^2)

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factor (a+b)^3-(2a+3b)^3

factor

(a + b)^{3} - (2 a + 3 b)^{3}

(- a - 2 b) (7 a^{2} + 19 ab + 13 b^{2})

Solution steps

(a + b)^{3} - (2 a + 3 b)^{3}

Apply Difference of Cubes Formula:

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

(a + b)^{3} - (2 a + 3 b)^{3} = ((a + b) - (2 a + 3 b)) ((a + b)^{2} + (a + b) (2 a + 3 b) + (2 a + 3 b)^{2})

= ((a + b) - (2 a + 3 b)) ((a + b)^{2} + (a + b) (2 a + 3 b) + (2 a + 3 b)^{2})

Refine

= (- a - 2 b) ((2 a + 3 b)^{2} + (a + b) (2 a + 3 b) + (a + b)^{2})

Expand

(a + b)^{2} + (a + b) (2 a + 3 b) + (2 a + 3 b)^{2} : 7 a^{2} + 19 ab + 13 b^{2}

= (- a - 2 b) (7 a^{2} + 19 ab + 13 b^{2})

(x - y)^{3} + 8 y^{3}

6 f e + 2 f h + 3 g e + g h

(- 5) + 3 a

m^{24} y^{3} - n^{3} z^{24}

x^{2} + 4 + 4

What is factor (a+b)^3-(2a+3b)^3 ?
The solution to factor (a+b)^3-(2a+3b)^3 is (-a-2b)(7a^2+19ab+13b^2)