Algebra Examples

$a (x + b) + x (b - a) = 2 b (2 a - x)$

Step 1

Simplify $a (x + b) + x (b - a)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$a x + a b + x (b - a) = 2 b (2 a - x)$

Step 1.1.2

Apply the distributive property.

$a x + a b + x b + x (- a) = 2 b (2 a - x)$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$a x + a b + x b - x a = 2 b (2 a - x)$

Step 1.2

Combine the opposite terms in $a x + a b + x b - x a$ .

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Step 1.2.1

Reorder the factors in the terms $a x$ and $- x a$ .

$a x + a b + x b - a x = 2 b (2 a - x)$

Step 1.2.2

Subtract $a x$ from $a x$ .

$a b + x b + 0 = 2 b (2 a - x)$

Step 1.2.3

Add $a b + x b$ and $0$ .

$a b + x b = 2 b (2 a - x)$

Step 2

Simplify $2 b (2 a - x)$ .

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

$a b + x b = 2 b (2 a) + 2 b (- x)$

Step 2.1.2

Reorder.

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Step 2.1.2.1

Rewrite using the commutative property of multiplication.

$a b + x b = 2 \cdot 2 b a + 2 b (- x)$

Step 2.1.2.2

Rewrite using the commutative property of multiplication.

$a b + x b = 2 \cdot 2 b a + 2 \cdot - 1 b x$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $2$ by $2$ .

$a b + x b = 4 b a + 2 \cdot - 1 b x$

Step 2.2.2

Multiply $2$ by $- 1$ .

$a b + x b = 4 b a - 2 b x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

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

$a b + x b + 2 b x = 4 b a$

Step 3.2

Add $x b$ and $2 b x$ .

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Step 3.2.1

Reorder $x$ and $b$ .

$a b + b x + 2 b x = 4 b a$

Step 3.2.2

Add $b x$ and $2 b x$ .

$a b + 3 b x = 4 b a$

Step 4

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

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Step 4.1

Subtract $a b$ from both sides of the equation.

$3 b x = 4 b a - a b$

Step 4.2

Subtract $a b$ from $4 b a$ .

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Step 4.2.1

Move $b$ .

$3 b x = 4 a b - a b$

Step 4.2.2

Subtract $a b$ from $4 a b$ .

$3 b x = 3 a b$

Step 5

Divide each term in $3 b x = 3 a b$ by $3 b$ and simplify.

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Step 5.1

Divide each term in $3 b x = 3 a b$ by $3 b$ .

$\frac{3 b x}{3 b} = \frac{3 a b}{3 b}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 b x}{3 b} = \frac{3 a b}{3 b}$

Step 5.2.1.2

Rewrite the expression.

$\frac{b x}{b} = \frac{3 a b}{3 b}$

Step 5.2.2

Cancel the common factor of $b$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{b x}{b} = \frac{3 a b}{3 b}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{3 a b}{3 b}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $3$ .

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Step 5.3.1.1

Cancel the common factor.

$x = \frac{3 a b}{3 b}$

Step 5.3.1.2

Rewrite the expression.

$x = \frac{a b}{b}$

Step 5.3.2

Cancel the common factor of $b$ .

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Step 5.3.2.1

Cancel the common factor.

$x = \frac{a b}{b}$

Step 5.3.2.2

Divide $a$ by $1$ .

$x = a$