Write in Standard Form (3c+7d)^2

${(3 c + 7 d)}^{2}$

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

Rewrite ${(3 c + 7 d)}^{2}$ as $(3 c + 7 d) (3 c + 7 d)$ .

$(3 c + 7 d) (3 c + 7 d)$

Step 3

Expand $(3 c + 7 d) (3 c + 7 d)$ using the FOIL Method.

Apply the distributive property.

$3 c (3 c + 7 d) + 7 d (3 c + 7 d)$

Apply the distributive property.

$3 c (3 c) + 3 c (7 d) + 7 d (3 c + 7 d)$

Apply the distributive property.

$3 c (3 c) + 3 c (7 d) + 7 d (3 c) + 7 d (7 d)$

Step 4

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 c \cdot c + 3 c (7 d) + 7 d (3 c) + 7 d (7 d)$

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

Move $c$ .

$3 \cdot 3 (c \cdot c) + 3 c (7 d) + 7 d (3 c) + 7 d (7 d)$

Multiply $c$ by $c$ .

$3 \cdot 3 c^{2} + 3 c (7 d) + 7 d (3 c) + 7 d (7 d)$

Multiply $3$ by $3$ .

$9 c^{2} + 3 c (7 d) + 7 d (3 c) + 7 d (7 d)$

Rewrite using the commutative property of multiplication.

$9 c^{2} + 3 \cdot 7 c d + 7 d (3 c) + 7 d (7 d)$

Multiply $3$ by $7$ .

$9 c^{2} + 21 c d + 7 d (3 c) + 7 d (7 d)$

Rewrite using the commutative property of multiplication.

$9 c^{2} + 21 c d + 7 \cdot 3 d c + 7 d (7 d)$

Multiply $7$ by $3$ .

$9 c^{2} + 21 c d + 21 d c + 7 d (7 d)$

Rewrite using the commutative property of multiplication.

$9 c^{2} + 21 c d + 21 d c + 7 \cdot 7 d \cdot d$

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

Move $d$ .

$9 c^{2} + 21 c d + 21 d c + 7 \cdot 7 (d \cdot d)$

Multiply $d$ by $d$ .

$9 c^{2} + 21 c d + 21 d c + 7 \cdot 7 d^{2}$

Multiply $7$ by $7$ .

$9 c^{2} + 21 c d + 21 d c + 49 d^{2}$

Add $21 c d$ and $21 d c$ .

Move $d$ .

$9 c^{2} + 21 c d + 21 c d + 49 d^{2}$

Add $21 c d$ and $21 c d$ .

$9 c^{2} + 42 c d + 49 d^{2}$

Write in Standard Form (3c+7d)^2

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