Algebra Examples

$(6 c + 5 d) (6 c - 5 d)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(6 c + 5 d) (6 c - 5 d)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 c (6 c - 5 d) + 5 d (6 c - 5 d)$

Step 2.2

Apply the distributive property.

$6 c (6 c) + 6 c (- 5 d) + 5 d (6 c - 5 d)$

Step 2.3

Apply the distributive property.

$6 c (6 c) + 6 c (- 5 d) + 5 d (6 c) + 5 d (- 5 d)$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $6 c (6 c) + 6 c (- 5 d) + 5 d (6 c) + 5 d (- 5 d)$ .

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Step 3.1.1

Reorder the factors in the terms $6 c (- 5 d)$ and $5 d (6 c)$ .

$6 c (6 c) - 5 \cdot 6 c d + 5 \cdot 6 c d + 5 d (- 5 d)$

Step 3.1.2

Add $- 5 \cdot 6 c d$ and $5 \cdot 6 c d$ .

$6 c (6 c) + 0 + 5 d (- 5 d)$

Step 3.1.3

Add $6 c (6 c)$ and $0$ .

$6 c (6 c) + 5 d (- 5 d)$

Step 3.2

Simplify each term.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$6 \cdot 6 c \cdot c + 5 d (- 5 d)$

Step 3.2.2

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

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Step 3.2.2.1

Move $c$ .

$6 \cdot 6 (c \cdot c) + 5 d (- 5 d)$

Step 3.2.2.2

Multiply $c$ by $c$ .

$6 \cdot 6 c^{2} + 5 d (- 5 d)$

Step 3.2.3

Multiply $6$ by $6$ .

$36 c^{2} + 5 d (- 5 d)$

Step 3.2.4

Rewrite using the commutative property of multiplication.

$36 c^{2} + 5 \cdot - 5 d \cdot d$

Step 3.2.5

Multiply $d$ by $d$ by adding the exponents.

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Step 3.2.5.1

Move $d$ .

$36 c^{2} + 5 \cdot - 5 (d \cdot d)$

Step 3.2.5.2

Multiply $d$ by $d$ .

$36 c^{2} + 5 \cdot - 5 d^{2}$

Step 3.2.6

Multiply $5$ by $- 5$ .

$36 c^{2} - 25 d^{2}$