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

The solution to (2x+1)^2+(3x-1)^2+2(2x+1)(3x-1) is 25x^2

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

simplify

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

25 x^{2}

Solution steps

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

Expand

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

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

Expand

(3 x - 1)^{2} : 9 x^{2} - 6 x + 1

= 4 x^{2} + 4 x + 1 + 9 x^{2} - 6 x + 1 + 2 (2 x + 1) (3 x - 1)

Expand

2 (2 x + 1) (3 x - 1) : 12 x^{2} + 2 x - 2

= 4 x^{2} + 4 x + 1 + 9 x^{2} - 6 x + 1 + 12 x^{2} + 2 x - 2

Group like terms

= 4 x^{2} + 9 x^{2} + 12 x^{2} + 4 x - 6 x + 2 x + 1 + 1 - 2

Add similar elements:

4 x^{2} + 9 x^{2} + 12 x^{2} = 25 x^{2}

= 25 x^{2} + 4 x - 6 x + 2 x + 1 + 1 - 2

Add similar elements:

4 x - 6 x + 2 x = 0

= 25 x^{2} + 1 + 1 - 2

Add the numbers:

1 + 1 - 2 = 0

= 25 x^{2}

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

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

4 a^{4} - 25 a^{2} \cdot b^{2} + 36 b^{4}

2 \frac{x ^{43}}{2}

x^{4} - 125 x \cdot y^{3}

What is (2x+1)^2+(3x-1)^2+2(2x+1)(3x-1) ?
The solution to (2x+1)^2+(3x-1)^2+2(2x+1)(3x-1) is 25x^2