Write in Standard Form (9c-2d)(9c-2d)

$(9 c - 2 d) (9 c - 2 d)$

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 $(9 c - 2 d) (9 c - 2 d)$ using the FOIL Method.

Apply the distributive property.

$9 c (9 c - 2 d) - 2 d (9 c - 2 d)$

Apply the distributive property.

$9 c (9 c) + 9 c (- 2 d) - 2 d (9 c - 2 d)$

Apply the distributive property.

$9 c (9 c) + 9 c (- 2 d) - 2 d (9 c) - 2 d (- 2 d)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 \cdot 9 c \cdot c + 9 c (- 2 d) - 2 d (9 c) - 2 d (- 2 d)$

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

Move $c$ .

$9 \cdot 9 (c \cdot c) + 9 c (- 2 d) - 2 d (9 c) - 2 d (- 2 d)$

Multiply $c$ by $c$ .

$9 \cdot 9 c^{2} + 9 c (- 2 d) - 2 d (9 c) - 2 d (- 2 d)$

Multiply $9$ by $9$ .

$81 c^{2} + 9 c (- 2 d) - 2 d (9 c) - 2 d (- 2 d)$

Rewrite using the commutative property of multiplication.

$81 c^{2} + 9 \cdot - 2 c d - 2 d (9 c) - 2 d (- 2 d)$

Multiply $9$ by $- 2$ .

$81 c^{2} - 18 c d - 2 d (9 c) - 2 d (- 2 d)$

Rewrite using the commutative property of multiplication.

$81 c^{2} - 18 c d - 2 \cdot 9 d c - 2 d (- 2 d)$

Multiply $- 2$ by $9$ .

$81 c^{2} - 18 c d - 18 d c - 2 d (- 2 d)$

Rewrite using the commutative property of multiplication.

$81 c^{2} - 18 c d - 18 d c - 2 \cdot - 2 d \cdot d$

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

Move $d$ .

$81 c^{2} - 18 c d - 18 d c - 2 \cdot - 2 (d \cdot d)$

Multiply $d$ by $d$ .

$81 c^{2} - 18 c d - 18 d c - 2 \cdot - 2 d^{2}$

Multiply $- 2$ by $- 2$ .

$81 c^{2} - 18 c d - 18 d c + 4 d^{2}$

Subtract $18 d c$ from $- 18 c d$ .

Move $d$ .

$81 c^{2} - 18 c d - 18 c d + 4 d^{2}$

Subtract $18 c d$ from $- 18 c d$ .

$81 c^{2} - 36 c d + 4 d^{2}$

Write in Standard Form (9c-2d)(9c-2d)

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