What is factor 4m^2-4m(n-m)+(n-m)^2 ?

The solution to factor 4m^2-4m(n-m)+(n-m)^2 is (3m-n)^2

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factor 4m^2-4m(n-m)+(n-m)^2

factor

4 m^{2} - 4 m (n - m) + (n - m)^{2}

(3 m - n)^{2}

Solution steps

4 m^{2} - 4 m (n - m) + (n - m)^{2}

(n - m)^{2} : n^{2} - 2 nm + m^{2}

= 4 m^{2} - 4 m (n - m) + n^{2} - 2 nm + m^{2}

Expand

- 4 m (n - m) : - 4 mn + 4 m^{2}

= 4 m^{2} - 4 mn + 4 m^{2} + n^{2} - 2 nm + m^{2}

Simplify

4 m^{2} - 4 mn + 4 m^{2} + n^{2} - 2 nm + m^{2} : 9 m^{2} - 6 mn + n^{2}

= 9 m^{2} - 6 mn + n^{2}

Rewrite

9 m^{2} - 6 mn + n^{2}

(3 m)^{2} - 2 \cdot 3 mn + n^{2}

= (3 m)^{2} - 2 \cdot 3 mn + n^{2}

Apply Perfect Square Formula:

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

a = 3 m, b = n

= (3 m - n)^{2}

8 x (x + 1) = - 1

- \frac{0.8 ( 10 )}{( 0.01 ( 10 ) ^{2} + 1 ) ^{2}}

4 x^{3} + 4 u

3 \leq 3 x - 4 < 2 x + 1

3 k^{2} - 21 k - 54

What is factor 4m^2-4m(n-m)+(n-m)^2 ?
The solution to factor 4m^2-4m(n-m)+(n-m)^2 is (3m-n)^2