Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$(b - 4) (b - 4) + (b - 1) (2 - b)$

Step 1.2

Expand $(b - 4) (b - 4)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$b (b - 4) - 4 (b - 4) + (b - 1) (2 - b)$

Step 1.2.2

Apply the distributive property.

$b \cdot b + b \cdot - 4 - 4 (b - 4) + (b - 1) (2 - b)$

Step 1.2.3

Apply the distributive property.

$b \cdot b + b \cdot - 4 - 4 b - 4 \cdot - 4 + (b - 1) (2 - b)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $b$ by $b$ .

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

Step 1.3.1.2

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

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

Step 1.3.1.3

Multiply $- 4$ by $- 4$ .

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

Step 1.3.2

Subtract $4 b$ from $- 4 b$ .

$b^{2} - 8 b + 16 + (b - 1) (2 - b)$

Step 1.4

Expand $(b - 1) (2 - b)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$b^{2} - 8 b + 16 + b (2 - b) - 1 (2 - b)$

Step 1.4.2

Apply the distributive property.

$b^{2} - 8 b + 16 + b \cdot 2 + b (- b) - 1 (2 - b)$

Step 1.4.3

Apply the distributive property.

$b^{2} - 8 b + 16 + b \cdot 2 + b (- b) - 1 \cdot 2 - 1 (- b)$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Move $2$ to the left of $b$ .

$b^{2} - 8 b + 16 + 2 \cdot b + b (- b) - 1 \cdot 2 - 1 (- b)$

Step 1.5.1.2

Rewrite using the commutative property of multiplication.

$b^{2} - 8 b + 16 + 2 b - b \cdot b - 1 \cdot 2 - 1 (- b)$

Step 1.5.1.3

Multiply $b$ by $b$ by adding the exponents.

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Step 1.5.1.3.1

Move $b$ .

$b^{2} - 8 b + 16 + 2 b - (b \cdot b) - 1 \cdot 2 - 1 (- b)$

Step 1.5.1.3.2

Multiply $b$ by $b$ .

$b^{2} - 8 b + 16 + 2 b - b^{2} - 1 \cdot 2 - 1 (- b)$

Step 1.5.1.4

Multiply $- 1$ by $2$ .

$b^{2} - 8 b + 16 + 2 b - b^{2} - 2 - 1 (- b)$

Step 1.5.1.5

Multiply $- 1 (- b)$ .

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Step 1.5.1.5.1

Multiply $- 1$ by $- 1$ .

$b^{2} - 8 b + 16 + 2 b - b^{2} - 2 + 1 b$

Step 1.5.1.5.2

Multiply $b$ by $1$ .

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

Step 1.5.2

Add $2 b$ and $b$ .

$b^{2} - 8 b + 16 + 3 b - b^{2} - 2$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $b^{2} - 8 b + 16 + 3 b - b^{2} - 2$ .

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Step 2.1.1

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

$- 8 b + 16 + 3 b + 0 - 2$

Step 2.1.2

Add $- 8 b + 16 + 3 b$ and $0$ .

$- 8 b + 16 + 3 b - 2$

Step 2.2

Add $- 8 b$ and $3 b$ .

$- 5 b + 16 - 2$

Step 2.3

Subtract $2$ from $16$ .

$- 5 b + 14$