Simplify (b-4)^2+(b-1)(2-b)

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

Step 1

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ .

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

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

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

Multiply $- 4$ by $- 4$ .

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

Rewrite using the commutative property of multiplication.

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $- 1 (- b)$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $b$ by $1$ .

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

Add $2 b$ and $b$ .

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

Step 2

Simplify by adding terms.

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

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

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

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

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

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

$- 5 b + 16 - 2$

Subtract $2$ from $16$ .

$- 5 b + 14$

Simplify (b-4)^2+(b-1)(2-b)

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