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

The solution to factor (a^2+2a)^2-2(a^2+2a)-3 is (a+1)^2(a-1)(a+3)

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

factor

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

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

Solution steps

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

Break the expression into groups

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

Factor out

(a^{2} + 2 a)

from

(a^{2} + 2 a)^{2} + (a^{2} + 2 a) : (a^{2} + 2 a) ((a^{2} + 2 a) + 1)

Factor out

- 3

from

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

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

Factor out common term

(a^{2} + 2 a) + 1

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

Refine

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

Factor

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

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

Factor

a^{2} + 2 a + 1 : (a + 1)^{2}

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

Factor

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

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

2 x^{2} < 5 x + 3

175

3 (2 + 5 (z - 1)) = 4 (5 (1 - z) + 1)

6 x^{2} = x + 2

b^{2} - 12 b + 27

What is factor (a^2+2a)^2-2(a^2+2a)-3 ?
The solution to factor (a^2+2a)^2-2(a^2+2a)-3 is (a+1)^2(a-1)(a+3)