Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(4 b - 1)}^{2}$ as $(4 b - 1) (4 b - 1)$ .

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

Step 1.2

Expand $(4 b - 1) (4 b - 1)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $b$ .

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

Step 1.3.1.2.2

Multiply $b$ by $b$ .

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

Step 1.3.1.3

Multiply $4$ by $4$ .

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

Step 1.3.1.4

Multiply $- 1$ by $4$ .

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

Step 1.3.1.5

Multiply $4$ by $- 1$ .

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

Step 1.3.1.6

Multiply $- 1$ by $- 1$ .

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

Step 1.3.2

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

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify.

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Step 1.5.1

Multiply $16$ by $- 1$ .

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

Step 1.5.2

Multiply $- 8$ by $- 1$ .

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

Step 1.5.3

Multiply $- 1$ by $1$ .

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

Step 2

Combine the opposite terms in $16 b^{2} + 1 - 16 b^{2} + 8 b - 1$ .

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Step 2.1

Subtract $16 b^{2}$ from $16 b^{2}$ .

$0 + 1 + 8 b - 1$

Step 2.2

Add $0$ and $1$ .

$1 + 8 b - 1$

Step 2.3

Subtract $1$ from $1$ .

$8 b + 0$

Step 2.4

Add $8 b$ and $0$ .

$8 b$