What is factor q^2a^2+2q^2+27a-9a^2-3q^2a-18 ?

The solution to factor q^2a^2+2q^2+27a-9a^2-3q^2a-18 is (a-1)(a-2)(q+3)(q-3)

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factor q^2a^2+2q^2+27a-9a^2-3q^2a-18

factor

q^{2} a^{2} + 2 q^{2} + 27 a - 9 a^{2} - 3 q^{2} a - 18

(a - 1) (a - 2) (q + 3) (q - 3)

Solution steps

q^{2} a^{2} + 2 q^{2} + 27 a - 9 a^{2} - 3 q^{2} a - 18

Group by common factors

= q^{2} a^{2} - 3 q^{2} a + 2 q^{2} - 9 a^{2} + 27 a - 18

= (q^{2} a^{2} - 3 q^{2} a + 2 q^{2}) + (- 9 a^{2} + 27 a - 18)

Factor out

q^{2}

from

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

Factor out

- 9

from

- 9 a^{2} + 27 a - 18 : - 9 (a^{2} - 3 a + 2)

= q^{2} (a^{2} - 3 a + 2) - 9 (a^{2} - 3 a + 2)

Factor out common term

a^{2} - 3 a + 2

= (a^{2} - 3 a + 2) (q^{2} - 9)

Factor

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

= (a - 1) (a - 2) (q^{2} - 9)

Factor

q^{2} - 9 : (q + 3) (q - 3)

= (a - 1) (a - 2) (q + 3) (q - 3)

3 x^{7} - 27 x

5 y^{- 3}

x^{2} + 8 x + 16 = 3

x - 20 > 24

18 x^{2} - 57 x + 35

What is factor q^2a^2+2q^2+27a-9a^2-3q^2a-18 ?
The solution to factor q^2a^2+2q^2+27a-9a^2-3q^2a-18 is (a-1)(a-2)(q+3)(q-3)