Find the Product (8x^2y+9m^3)^2

${(8 x^{2} y + 9 m^{3})}^{2}$

Step 1

Rewrite ${(8 x^{2} y + 9 m^{3})}^{2}$ as $(8 x^{2} y + 9 m^{3}) (8 x^{2} y + 9 m^{3})$ .

$(8 x^{2} y + 9 m^{3}) (8 x^{2} y + 9 m^{3})$

Step 2

Expand $(8 x^{2} y + 9 m^{3}) (8 x^{2} y + 9 m^{3})$ using the FOIL Method.

Apply the distributive property.

$8 x^{2} y (8 x^{2} y + 9 m^{3}) + 9 m^{3} (8 x^{2} y + 9 m^{3})$

Apply the distributive property.

$8 x^{2} y (8 x^{2} y) + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y + 9 m^{3})$

Apply the distributive property.

$8 x^{2} y (8 x^{2} y) + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $x^{2}$ .

$8 (x^{2} x^{2}) y (8 y) + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

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

$8 x^{2 + 2} y (8 y) + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Add $2$ and $2$ .

$8 x^{4} y (8 y) + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{4} (y \cdot y) \cdot 8 + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Multiply $y$ by $y$ .

$8 x^{4} y^{2} \cdot 8 + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Multiply $8$ by $8$ .

$64 x^{4} y^{2} + 8 x^{2} y (9 m^{3}) + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Multiply $9$ by $8$ .

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 9 m^{3} (8 x^{2} y) + 9 m^{3} (9 m^{3})$

Multiply $8$ by $9$ .

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} (x^{2} y) + 9 m^{3} (9 m^{3})$

Rewrite using the commutative property of multiplication.

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} x^{2} y + 9 \cdot 9 m^{3} m^{3}$

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

Move $m^{3}$ .

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} x^{2} y + 9 \cdot 9 (m^{3} m^{3})$

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

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} x^{2} y + 9 \cdot 9 m^{3 + 3}$

Add $3$ and $3$ .

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} x^{2} y + 9 \cdot 9 m^{6}$

Multiply $9$ by $9$ .

$64 x^{4} y^{2} + 72 x^{2} y m^{3} + 72 m^{3} x^{2} y + 81 m^{6}$

Add $72 x^{2} y m^{3}$ and $72 m^{3} x^{2} y$ .

Move $x^{2}$ .

$64 x^{4} y^{2} + 72 m^{3} x^{2} y + 72 m^{3} x^{2} y + 81 m^{6}$

Add $72 m^{3} x^{2} y$ and $72 m^{3} x^{2} y$ .

$64 x^{4} y^{2} + 144 m^{3} x^{2} y + 81 m^{6}$

Find the Product (8x^2y+9m^3)^2

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