What is factor (m+n)^2+1/4-(m+n) ?

The solution to factor (m+n)^2+1/4-(m+n) is (m+n-0.5)^2

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factor (m+n)^2+1/4-(m+n)

factor

(m + n)^{2} + \frac{1}{4} - (m + n)

(m + n - 0.5)^{2}

Solution steps

(m + n)^{2} + \frac{1}{4} - (m + n)

Write in the standard form

a x^{2} + b x + c

= (m + n)^{2} - (m + n) + \frac{1}{4}

Rewrite

(m + n)^{2} - (m + n) + \frac{1}{4}

(m + n)^{2} - 2 (m + n) \cdot 0.5 + (\frac{1}{4})^{2}

= (m + n)^{2} - 2 (m + n) \cdot 0.5 + (\frac{1}{4})^{2}

Apply Perfect Square Formula:

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

a = (m + n), b = 0.5

= ((m + n) - 0.5)^{2}

Refine

= (m + n - 0.5)^{2}

4 + ∣ t + 2 ∣ < 11

(\frac{2}{3})^{\frac{2}{3}}

80 - 50 x

- (- 4)^{3}

8 n + 16.2 = 1.6

What is factor (m+n)^2+1/4-(m+n) ?
The solution to factor (m+n)^2+1/4-(m+n) is (m+n-0.5)^2