Basic Math Examples

$(4 c + 3 t) (4 c - 3 t)$

Step 1

Expand $(4 c + 3 t) (4 c - 3 t)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 c (4 c - 3 t) + 3 t (4 c - 3 t)$

Step 1.2

Apply the distributive property.

$4 c (4 c) + 4 c (- 3 t) + 3 t (4 c - 3 t)$

Step 1.3

Apply the distributive property.

$4 c (4 c) + 4 c (- 3 t) + 3 t (4 c) + 3 t (- 3 t)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $4 c (4 c) + 4 c (- 3 t) + 3 t (4 c) + 3 t (- 3 t)$ .

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Step 2.1.1

Reorder the factors in the terms $4 c (- 3 t)$ and $3 t (4 c)$ .

$4 c (4 c) - 3 \cdot 4 c t + 3 \cdot 4 c t + 3 t (- 3 t)$

Step 2.1.2

Add $- 3 \cdot 4 c t$ and $3 \cdot 4 c t$ .

$4 c (4 c) + 0 + 3 t (- 3 t)$

Step 2.1.3

Add $4 c (4 c)$ and $0$ .

$4 c (4 c) + 3 t (- 3 t)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 4 c \cdot c + 3 t (- 3 t)$

Step 2.2.2

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

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Step 2.2.2.1

Move $c$ .

$4 \cdot 4 (c \cdot c) + 3 t (- 3 t)$

Step 2.2.2.2

Multiply $c$ by $c$ .

$4 \cdot 4 c^{2} + 3 t (- 3 t)$

Step 2.2.3

Multiply $4$ by $4$ .

$16 c^{2} + 3 t (- 3 t)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$16 c^{2} + 3 \cdot - 3 t \cdot t$

Step 2.2.5

Multiply $t$ by $t$ by adding the exponents.

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Step 2.2.5.1

Move $t$ .

$16 c^{2} + 3 \cdot - 3 (t \cdot t)$

Step 2.2.5.2

Multiply $t$ by $t$ .

$16 c^{2} + 3 \cdot - 3 t^{2}$

Step 2.2.6

Multiply $3$ by $- 3$ .

$16 c^{2} - 9 t^{2}$