What is (2x-1)^2+(x-3)^2 ?

The solution to (2x-1)^2+(x-3)^2 is 5x^2-10x+10

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simplify (2x-1)^2+(x-3)^2

simplify

(2 x - 1)^{2} + (x - 3)^{2}

5 x^{2} - 10 x + 10

Solution steps

(2 x - 1)^{2} + (x - 3)^{2}

Expand

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

= 4 x^{2} - 4 x + 1 + (x - 3)^{2}

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= 4 x^{2} - 4 x + 1 + x^{2} - 6 x + 9

Group like terms

= 4 x^{2} + x^{2} - 4 x - 6 x + 1 + 9

Add similar elements:

4 x^{2} + x^{2} = 5 x^{2}

= 5 x^{2} - 4 x - 6 x + 1 + 9

Add similar elements:

- 4 x - 6 x = - 10 x

= 5 x^{2} - 10 x + 1 + 9

Add the numbers:

1 + 9 = 10

= 5 x^{2} - 10 x + 10

x^{2} + 12 x + 32

- \frac{4}{3} \times 3

6 a^{2} + 27

(m + \frac{1}{m})^{6}

(\times + 1)^{2}