Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(4 c + 1)}^{2}$ as $(4 c + 1) (4 c + 1)$ .

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

Step 1.2

Expand $(4 c + 1) (4 c + 1)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

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.

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

Step 1.3.1.2

Multiply $c$ by $c$ by adding the exponents.

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Step 1.3.1.2.1

Move $c$ .

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

Step 1.3.1.2.2

Multiply $c$ by $c$ .

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

Step 1.3.1.3

Multiply $4$ by $4$ .

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

Step 1.3.1.4

Multiply $4$ by $1$ .

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

Step 1.3.1.5

Multiply $4 c$ by $1$ .

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

Step 1.3.1.6

Multiply $1$ by $1$ .

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

Step 1.3.2

Add $4 c$ and $4 c$ .

$16 c^{2} + 8 c + 1 - 4 c (c + 2)$

Step 1.4

Apply the distributive property.

$16 c^{2} + 8 c + 1 - 4 c \cdot c - 4 c \cdot 2$

Step 1.5

Multiply $c$ by $c$ by adding the exponents.

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Step 1.5.1

Move $c$ .

$16 c^{2} + 8 c + 1 - 4 (c \cdot c) - 4 c \cdot 2$

Step 1.5.2

Multiply $c$ by $c$ .

$16 c^{2} + 8 c + 1 - 4 c^{2} - 4 c \cdot 2$

Step 1.6

Multiply $2$ by $- 4$ .

$16 c^{2} + 8 c + 1 - 4 c^{2} - 8 c$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $16 c^{2} + 8 c + 1 - 4 c^{2} - 8 c$ .

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Step 2.1.1

Subtract $8 c$ from $8 c$ .

$16 c^{2} + 1 - 4 c^{2} + 0$

Step 2.1.2

Add $16 c^{2} + 1 - 4 c^{2}$ and $0$ .

$16 c^{2} + 1 - 4 c^{2}$

Step 2.2

Subtract $4 c^{2}$ from $16 c^{2}$ .

$12 c^{2} + 1$