Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $2 x + x (2 x - 4) + y = x^{2}$ .

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

Step 1.2

Simplify $2 x + x (2 x - 4) + y$ .

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Apply the distributive property.

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

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$2 x + 2 x \cdot x + x \cdot - 4 + y = x^{2}$

Step 1.2.1.3

Move $- 4$ to the left of $x$ .

$2 x + 2 x \cdot x - 4 \cdot x + y = x^{2}$

Step 1.2.1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1.4.1

Move $x$ .

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

Step 1.2.1.4.2

Multiply $x$ by $x$ .

$2 x + 2 x^{2} - 4 \cdot x + y = x^{2}$

$2 x + 2 x^{2} - 4 x + y = x^{2}$

Step 1.2.2

Subtract $4 x$ from $2 x$ .

$2 x^{2} - 2 x + y = x^{2}$

Step 1.3

Move all terms not containing $y$ to the right side of the equation.

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Step 1.3.1

Subtract $2 x^{2}$ from both sides of the equation.

$- 2 x + y = x^{2} - 2 x^{2}$

Step 1.3.2

Add $2 x$ to both sides of the equation.

$y = x^{2} - 2 x^{2} + 2 x$

Step 1.3.3

Subtract $2 x^{2}$ from $x^{2}$ .

$y = - x^{2} + 2 x$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $- x^{2} + 2 x$ .

$y = - x^{2} + 2 x$

Step 4