Algebra Examples

u^{2} - 4 u + 4

$u^{2} - 4 u + 4$

Step 1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

u^{2} - 4 u + 2^{2}

$u^{2} - 4 u + 2^{2}$

Step 2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

4 u = 2 \cdot u \cdot 2

$4 u = 2 \cdot u \cdot 2$

Step 3

Rewrite the polynomial.

u^{2} - 2 \cdot u \cdot 2 + 2^{2}

$u^{2} - 2 \cdot u \cdot 2 + 2^{2}$

Step 4

Factor using the perfect square trinomial rule

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

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

a = u

$a = u$ and

b = 2

$b = 2$ .

{(u - 2)}^{2}

${(u - 2)}^{2}$