Finite Math Examples

${(4 - (a - b))}^{2}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

${(4 - a - - b)}^{2}$

Step 1.1.2

Multiply $- - b$ .

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Step 1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.2.2

Multiply $b$ by $1$ .

${(4 - a + b)}^{2}$

Step 1.2

Rewrite ${(4 - a + b)}^{2}$ as $(4 - a + b) (4 - a + b)$ .

$(4 - a + b) (4 - a + b)$

Step 2

Expand $(4 - a + b) (4 - a + b)$ by multiplying each term in the first expression by each term in the second expression.

$4 \cdot 4 + 4 (- a) + 4 b - a \cdot 4 - a (- a) - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $4$ by $4$ .

$16 + 4 (- a) + 4 b - a \cdot 4 - a (- a) - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.2

Multiply $- 1$ by $4$ .

$16 - 4 a + 4 b - a \cdot 4 - a (- a) - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.3

Multiply $4$ by $- 1$ .

$16 - 4 a + 4 b - 4 a - a (- a) - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$16 - 4 a + 4 b - 4 a - 1 \cdot - 1 a \cdot a - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.5

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1.5.1

Move $a$ .

$16 - 4 a + 4 b - 4 a - 1 \cdot - 1 (a \cdot a) - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.5.2

Multiply $a$ by $a$ .

$16 - 4 a + 4 b - 4 a - 1 \cdot - 1 a^{2} - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.6

Multiply $- 1$ by $- 1$ .

$16 - 4 a + 4 b - 4 a + 1 a^{2} - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.7

Multiply $a^{2}$ by $1$ .

$16 - 4 a + 4 b - 4 a + a^{2} - a b + b \cdot 4 + b (- a) + b \cdot b$

Step 3.1.8

Move $4$ to the left of $b$ .

$16 - 4 a + 4 b - 4 a + a^{2} - a b + 4 \cdot b + b (- a) + b \cdot b$

Step 3.1.9

Rewrite using the commutative property of multiplication.

$16 - 4 a + 4 b - 4 a + a^{2} - a b + 4 b - b a + b \cdot b$

Step 3.1.10

Multiply $b$ by $b$ .

$16 - 4 a + 4 b - 4 a + a^{2} - a b + 4 b - b a + b^{2}$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

Subtract $4 a$ from $- 4 a$ .

$16 - 8 a + 4 b + a^{2} - a b + 4 b - b a + b^{2}$

Step 3.2.2

Add $4 b$ and $4 b$ .

$16 - 8 a + 8 b + a^{2} - a b - b a + b^{2}$

Step 4

Subtract $b a$ from $- a b$ .

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Step 4.1

Move $b$ .

$16 - 8 a + 8 b + a^{2} - a b - a b + b^{2}$

Step 4.2

Subtract $a b$ from $- a b$ .

$16 - 8 a + 8 b + a^{2} - 2 a b + b^{2}$

Step 5

Move $16$ .

$- 8 a + 8 b + a^{2} - 2 a b + b^{2} + 16$

Step 6

Move $8 b$ .

$- 8 a + a^{2} - 2 a b + b^{2} + 8 b + 16$

Step 7

Move $- 8 a$ .

$a^{2} - 2 a b + b^{2} - 8 a + 8 b + 16$