What is factor 9(a-b)^2+12(a-b)(a+b)+4(a+b)^2 ?

The solution to factor 9(a-b)^2+12(a-b)(a+b)+4(a+b)^2 is (5a-b)^2

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factor 9(a-b)^2+12(a-b)(a+b)+4(a+b)^2

factor

9 (a - b)^{2} + 12 (a - b) (a + b) + 4 (a + b)^{2}

(5 a - b)^{2}

Solution steps

9 (a - b)^{2} + 12 (a - b) (a + b) + 4 (a + b)^{2}

(a - b)^{2} : a^{2} - 2 ab + b^{2}

= 9 (a^{2} - 2 ab + b^{2}) + 12 (a - b) (a + b) + 4 (a + b)^{2}

(a + b)^{2} : a^{2} + 2 ab + b^{2}

= 9 (a^{2} - 2 ab + b^{2}) + 12 (a - b) (a + b) + 4 (a^{2} + 2 ab + b^{2})

Expand

9 (a^{2} - 2 ab + b^{2}) : 9 a^{2} - 18 ab + 9 b^{2}

= 9 a^{2} - 18 ab + 9 b^{2} + 12 (a - b) (a + b) + 4 (a^{2} + 2 ab + b^{2})

Expand

12 (a - b) (a + b) : 12 a^{2} - 12 b^{2}

= 9 a^{2} - 18 ab + 9 b^{2} + 12 a^{2} - 12 b^{2} + 4 (a^{2} + 2 ab + b^{2})

Expand

4 (a^{2} + 2 ab + b^{2}) : 4 a^{2} + 8 ab + 4 b^{2}

= 9 a^{2} - 18 ab + 9 b^{2} + 12 a^{2} - 12 b^{2} + 4 a^{2} + 8 ab + 4 b^{2}

Simplify

9 a^{2} - 18 ab + 9 b^{2} + 12 a^{2} - 12 b^{2} + 4 a^{2} + 8 ab + 4 b^{2} : 25 a^{2} - 10 ab + b^{2}

= 25 a^{2} - 10 ab + b^{2}

Rewrite

25 a^{2} - 10 ab + b^{2}

(5 a)^{2} - 2 \cdot 5 ab + b^{2}

= (5 a)^{2} - 2 \cdot 5 ab + b^{2}

Apply Perfect Square Formula:

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

a = 5 a, b = b

= (5 a - b)^{2}

- 10 x = 2 x^{2}

\frac{1}{x} < 2

4 x^{2} = 100

3 m^{- 2}

\frac{9}{8} - \frac{5}{6}

What is factor 9(a-b)^2+12(a-b)(a+b)+4(a+b)^2 ?
The solution to factor 9(a-b)^2+12(a-b)(a+b)+4(a+b)^2 is (5a-b)^2