Find the Product (4x^3+7y^3z^4)^2

${(4 x^{3} + 7 y^{3} z^{4})}^{2}$

Step 1

Rewrite ${(4 x^{3} + 7 y^{3} z^{4})}^{2}$ as $(4 x^{3} + 7 y^{3} z^{4}) (4 x^{3} + 7 y^{3} z^{4})$ .

$(4 x^{3} + 7 y^{3} z^{4}) (4 x^{3} + 7 y^{3} z^{4})$

Step 2

Expand $(4 x^{3} + 7 y^{3} z^{4}) (4 x^{3} + 7 y^{3} z^{4})$ using the FOIL Method.

Apply the distributive property.

$4 x^{3} (4 x^{3} + 7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3} + 7 y^{3} z^{4})$

Apply the distributive property.

$4 x^{3} (4 x^{3}) + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3} + 7 y^{3} z^{4})$

Apply the distributive property.

$4 x^{3} (4 x^{3}) + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x^{3} x^{3} + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

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

Move $x^{3}$ .

$4 \cdot 4 (x^{3} x^{3}) + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

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

$4 \cdot 4 x^{3 + 3} + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

Add $3$ and $3$ .

$4 \cdot 4 x^{6} + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

Multiply $4$ by $4$ .

$16 x^{6} + 4 x^{3} (7 y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

Multiply $7$ by $4$ .

$16 x^{6} + 28 x^{3} (y^{3} z^{4}) + 7 y^{3} z^{4} (4 x^{3}) + 7 y^{3} z^{4} (7 y^{3} z^{4})$

Multiply $4$ by $7$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{3} z^{4} (7 y^{3} z^{4})$

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

Move $y^{3}$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 (y^{3} y^{3}) z^{4} (7 z^{4})$

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

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{3 + 3} z^{4} (7 z^{4})$

Add $3$ and $3$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{6} z^{4} (7 z^{4})$

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

Move $z^{4}$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{6} (z^{4} z^{4}) \cdot 7$

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

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{6} z^{4 + 4} \cdot 7$

Add $4$ and $4$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 7 y^{6} z^{8} \cdot 7$

Multiply $7$ by $7$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 y^{3} z^{4} x^{3} + 49 y^{6} z^{8}$

Add $28 x^{3} y^{3} z^{4}$ and $28 y^{3} z^{4} x^{3}$ .

Move $y^{3}$ .

$16 x^{6} + 28 x^{3} y^{3} z^{4} + 28 x^{3} y^{3} z^{4} + 49 y^{6} z^{8}$

Add $28 x^{3} y^{3} z^{4}$ and $28 x^{3} y^{3} z^{4}$ .

$16 x^{6} + 56 x^{3} y^{3} z^{4} + 49 y^{6} z^{8}$

Find the Product (4x^3+7y^3z^4)^2

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