What is factor (a+b)^3-(30+4b)^3 ?

The solution to factor (a+b)^3-(30+4b)^3 is (-3b+a-30)(21b^2+6ab+270b+a^2+30a+900)

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factor (a+b)^3-(30+4b)^3

factor

(a + b)^{3} - (30 + 4 b)^{3}

(- 3 b + a - 30) (21 b^{2} + 6 ab + 270 b + a^{2} + 30 a + 900)

Solution steps

(a + b)^{3} - (30 + 4 b)^{3}

Apply Difference of Cubes Formula:

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

(a + b)^{3} - (30 + 4 b)^{3} = ((a + b) - (30 + 4 b)) ((a + b)^{2} + (30 + 4 b) (a + b) + (30 + 4 b)^{2})

= ((a + b) - (30 + 4 b)) ((30 + 4 b)^{2} + (30 + 4 b) (a + b) + (a + b)^{2})

Refine

= (a - 3 b - 30) ((4 b + 30)^{2} + (4 b + 30) (a + b) + (a + b)^{2})

(30 + 4 b) (a + b) = 2 (2 b + 15) (a + b)

(30 + 4 b)^{2} = 4 (2 b + 15)^{2}

= (a - 3 b - 30) (2 (2 b + 15) (a + b) + 4 (2 b + 15)^{2} + (a + b)^{2})

Expand

(a + b)^{2} + 2 (2 b + 15) (a + b) + 4 (2 b + 15)^{2} : 21 b^{2} + 6 ab + 270 b + a^{2} + 30 a + 900

= (a - 3 b - 30) (a^{2} + 6 ab + 30 a + 21 b^{2} + 270 b + 900)

x^{2} + 10 + 24

(5 a + 1)^{2} - 2 (5 a + 1) - 3

[2.8]

6 x^{2} z - 15 x^{2} + 2 yz - 5 y

A (1.2)

What is factor (a+b)^3-(30+4b)^3 ?
The solution to factor (a+b)^3-(30+4b)^3 is (-3b+a-30)(21b^2+6ab+270b+a^2+30a+900)