Simplify 9b(b-1)-(3b+2)^2

$9 b (b - 1) - {(3 b + 2)}^{2}$

Step 1

Simplify each term.

Apply the distributive property.

$9 b \cdot b + 9 b \cdot - 1 - {(3 b + 2)}^{2}$

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

Move $b$ .

$9 (b \cdot b) + 9 b \cdot - 1 - {(3 b + 2)}^{2}$

Multiply $b$ by $b$ .

$9 b^{2} + 9 b \cdot - 1 - {(3 b + 2)}^{2}$

Multiply $- 1$ by $9$ .

$9 b^{2} - 9 b - {(3 b + 2)}^{2}$

Rewrite ${(3 b + 2)}^{2}$ as $(3 b + 2) (3 b + 2)$ .

$9 b^{2} - 9 b - ((3 b + 2) (3 b + 2))$

Expand $(3 b + 2) (3 b + 2)$ using the FOIL Method.

Apply the distributive property.

$9 b^{2} - 9 b - (3 b (3 b + 2) + 2 (3 b + 2))$

Apply the distributive property.

$9 b^{2} - 9 b - (3 b (3 b) + 3 b \cdot 2 + 2 (3 b + 2))$

Apply the distributive property.

$9 b^{2} - 9 b - (3 b (3 b) + 3 b \cdot 2 + 2 (3 b) + 2 \cdot 2)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 b^{2} - 9 b - (3 \cdot 3 b \cdot b + 3 b \cdot 2 + 2 (3 b) + 2 \cdot 2)$

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

Move $b$ .

$9 b^{2} - 9 b - (3 \cdot 3 (b \cdot b) + 3 b \cdot 2 + 2 (3 b) + 2 \cdot 2)$

Multiply $b$ by $b$ .

$9 b^{2} - 9 b - (3 \cdot 3 b^{2} + 3 b \cdot 2 + 2 (3 b) + 2 \cdot 2)$

Multiply $3$ by $3$ .

$9 b^{2} - 9 b - (9 b^{2} + 3 b \cdot 2 + 2 (3 b) + 2 \cdot 2)$

Multiply $2$ by $3$ .

$9 b^{2} - 9 b - (9 b^{2} + 6 b + 2 (3 b) + 2 \cdot 2)$

Multiply $3$ by $2$ .

$9 b^{2} - 9 b - (9 b^{2} + 6 b + 6 b + 2 \cdot 2)$

Multiply $2$ by $2$ .

$9 b^{2} - 9 b - (9 b^{2} + 6 b + 6 b + 4)$

Add $6 b$ and $6 b$ .

$9 b^{2} - 9 b - (9 b^{2} + 12 b + 4)$

Apply the distributive property.

$9 b^{2} - 9 b - (9 b^{2}) - (12 b) - 1 \cdot 4$

Simplify.

Multiply $9$ by $- 1$ .

$9 b^{2} - 9 b - 9 b^{2} - (12 b) - 1 \cdot 4$

Multiply $12$ by $- 1$ .

$9 b^{2} - 9 b - 9 b^{2} - 12 b - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$9 b^{2} - 9 b - 9 b^{2} - 12 b - 4$

Step 2

Simplify by adding terms.

Combine the opposite terms in $9 b^{2} - 9 b - 9 b^{2} - 12 b - 4$ .

Subtract $9 b^{2}$ from $9 b^{2}$ .

$- 9 b + 0 - 12 b - 4$

Add $- 9 b$ and $0$ .

$- 9 b - 12 b - 4$

Subtract $12 b$ from $- 9 b$ .

$- 21 b - 4$

Simplify 9b(b-1)-(3b+2)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.