Solve (1/4a-1/2b+1)^2 - ScanMath

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Question

Simplify the expression

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1 - \frac{1}{4} ab + \frac{1}{2} a - b

Evaluate

(\frac{1}{4} a - \frac{1}{2} b + 1)^{2}

Use (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 ab + 2 a c + 2 b c to expand the expression

(\frac{1}{4} a)^{2} + (- \frac{1}{2} b)^{2} + 1^{2} + 2 \times \frac{1}{4} a (- \frac{1}{2} b) + 2 \times \frac{1}{4} a \times 1 + 2 (- \frac{1}{2} b) \times 1

Calculate

More Steps

\frac{1}{16} a^{2} + (- \frac{1}{2} b)^{2} + 1^{2} + 2 \times \frac{1}{4} a (- \frac{1}{2} b) + 2 \times \frac{1}{4} a \times 1 + 2 (- \frac{1}{2} b) \times 1

Calculate

More Steps

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1^{2} + 2 \times \frac{1}{4} a (- \frac{1}{2} b) + 2 \times \frac{1}{4} a \times 1 + 2 (- \frac{1}{2} b) \times 1

Calculate

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1 + 2 \times \frac{1}{4} a (- \frac{1}{2} b) + 2 \times \frac{1}{4} a \times 1 + 2 (- \frac{1}{2} b) \times 1

Calculate

More Steps

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1 - \frac{1}{4} ab + 2 \times \frac{1}{4} a \times 1 + 2 (- \frac{1}{2} b) \times 1

Calculate

More Steps

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1 - \frac{1}{4} ab + \frac{1}{2} a + 2 (- \frac{1}{2} b) \times 1

Solution

More Steps

\frac{1}{16} a^{2} + \frac{1}{4} b^{2} + 1 - \frac{1}{4} ab + \frac{1}{2} a - b

Show Solution

Factor the expression

\frac{1}{16} (a - 2 b + 4)^{2}

Show Solution