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

The solution to factor (m+a)^2-2(m+a)(a+b)+(a+b)^2 is (m-b)^2

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

factor

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

(m - b)^{2}

Solution steps

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

(m + a)^{2} : m^{2} + 2 ma + a^{2}

= m^{2} + 2 ma + a^{2} - 2 (m + a) (a + b) + (a + b)^{2}

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

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

Expand

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

= m^{2} + 2 ma + a^{2} - 2 ma - 2 mb - 2 a^{2} - 2 ab + a^{2} + 2 ab + b^{2}

Simplify

m^{2} + 2 ma + a^{2} - 2 ma - 2 mb - 2 a^{2} - 2 ab + a^{2} + 2 ab + b^{2} : m^{2} + b^{2} - 2 mb

= m^{2} + b^{2} - 2 mb

Apply Perfect Square Formula:

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

a = m, b = b

= (m - b)^{2}

x^{2} - 20 x + 72 = - 3 x

4 (- 1)^{4} - 24 (- 1)^{3} + 14 (- 1)^{2} - 50 (- 1) - 70

m^{2} - 5 m + 6

\frac{6 x + 3}{4 x - 2} < 12

\frac{9}{25}

What is factor (m+a)^2-2(m+a)(a+b)+(a+b)^2 ?
The solution to factor (m+a)^2-2(m+a)(a+b)+(a+b)^2 is (m-b)^2