What is factor 4+4(x-y)+(x-y)^2 ?

The solution to factor 4+4(x-y)+(x-y)^2 is (x-y+2)^2

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factor 4+4(x-y)+(x-y)^2

factor

4 + 4 (x - y) + (x - y)^{2}

(x - y + 2)^{2}

Solution steps

4 + 4 (x - y) + (x - y)^{2}

Write in the standard form

a x^{2} + b x + c

= (x - y)^{2} + 4 (x - y) + 4

Rewrite

(x - y)^{2} + 4 (x - y) + 4

(x - y)^{2} + 2 (x - y) \cdot 2 + 2^{2}

= (x - y)^{2} + 2 (x - y) \cdot 2 + 2^{2}

Apply Perfect Square Formula:

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

a = (x - y), b = 2

= ((x - y) + 2)^{2}

Refine

= (x + 2 - y)^{2}

16 a^{3} b^{7} + 2 a^{6} b^{4} - 22 a^{4} b^{5}

x^{2} - 3 x - 10 = 0

a^{2} + 5 a - 24

- 3 x + 2 \leq - 4

x^{2} + 8 x - 14 = 0

What is factor 4+4(x-y)+(x-y)^2 ?
The solution to factor 4+4(x-y)+(x-y)^2 is (x-y+2)^2