Find the Product (7a^2b^3+5x^4)^2

${(7 a^{2} b^{3} + 5 x^{4})}^{2}$

Step 1

Rewrite ${(7 a^{2} b^{3} + 5 x^{4})}^{2}$ as $(7 a^{2} b^{3} + 5 x^{4}) (7 a^{2} b^{3} + 5 x^{4})$ .

$(7 a^{2} b^{3} + 5 x^{4}) (7 a^{2} b^{3} + 5 x^{4})$

Step 2

Expand $(7 a^{2} b^{3} + 5 x^{4}) (7 a^{2} b^{3} + 5 x^{4})$ using the FOIL Method.

Apply the distributive property.

$7 a^{2} b^{3} (7 a^{2} b^{3} + 5 x^{4}) + 5 x^{4} (7 a^{2} b^{3} + 5 x^{4})$

Apply the distributive property.

$7 a^{2} b^{3} (7 a^{2} b^{3}) + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3} + 5 x^{4})$

Apply the distributive property.

$7 a^{2} b^{3} (7 a^{2} b^{3}) + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$7 (a^{2} a^{2}) b^{3} (7 b^{3}) + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 a^{2 + 2} b^{3} (7 b^{3}) + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Add $2$ and $2$ .

$7 a^{4} b^{3} (7 b^{3}) + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Multiply $b^{3}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$7 a^{4} (b^{3} b^{3}) \cdot 7 + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 a^{4} b^{3 + 3} \cdot 7 + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Add $3$ and $3$ .

$7 a^{4} b^{6} \cdot 7 + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Multiply $7$ by $7$ .

$49 a^{4} b^{6} + 7 a^{2} b^{3} (5 x^{4}) + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Multiply $5$ by $7$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 5 x^{4} (7 a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Multiply $7$ by $5$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} (a^{2} b^{3}) + 5 x^{4} (5 x^{4})$

Rewrite using the commutative property of multiplication.

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} a^{2} b^{3} + 5 \cdot 5 x^{4} x^{4}$

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} a^{2} b^{3} + 5 \cdot 5 (x^{4} x^{4})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} a^{2} b^{3} + 5 \cdot 5 x^{4 + 4}$

Add $4$ and $4$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} a^{2} b^{3} + 5 \cdot 5 x^{8}$

Multiply $5$ by $5$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 x^{4} a^{2} b^{3} + 25 x^{8}$

Add $35 a^{2} b^{3} x^{4}$ and $35 x^{4} a^{2} b^{3}$ .

Move $x^{4}$ .

$49 a^{4} b^{6} + 35 a^{2} b^{3} x^{4} + 35 a^{2} b^{3} x^{4} + 25 x^{8}$

Add $35 a^{2} b^{3} x^{4}$ and $35 a^{2} b^{3} x^{4}$ .

$49 a^{4} b^{6} + 70 a^{2} b^{3} x^{4} + 25 x^{8}$

Find the Product (7a^2b^3+5x^4)^2

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