Simplify (4x-6y^3)^2

${(4 x - 6 y^{3})}^{2}$

Step 1

Rewrite ${(4 x - 6 y^{3})}^{2}$ as $(4 x - 6 y^{3}) (4 x - 6 y^{3})$ .

$(4 x - 6 y^{3}) (4 x - 6 y^{3})$

Step 2

Expand $(4 x - 6 y^{3}) (4 x - 6 y^{3})$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 6 y^{3}) - 6 y^{3} (4 x - 6 y^{3})$

Apply the distributive property.

$4 x (4 x) + 4 x (- 6 y^{3}) - 6 y^{3} (4 x - 6 y^{3})$

Apply the distributive property.

$4 x (4 x) + 4 x (- 6 y^{3}) - 6 y^{3} (4 x) - 6 y^{3} (- 6 y^{3})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$4 \cdot 4 x^{2} + 4 x (- 6 y^{3}) - 6 y^{3} (4 x) - 6 y^{3} (- 6 y^{3})$

Multiply $4$ by $4$ .

$16 x^{2} + 4 x (- 6 y^{3}) - 6 y^{3} (4 x) - 6 y^{3} (- 6 y^{3})$

Rewrite using the commutative property of multiplication.

$16 x^{2} + 4 \cdot - 6 x y^{3} - 6 y^{3} (4 x) - 6 y^{3} (- 6 y^{3})$

Multiply $4$ by $- 6$ .

$16 x^{2} - 24 x y^{3} - 6 y^{3} (4 x) - 6 y^{3} (- 6 y^{3})$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 24 x y^{3} - 6 \cdot 4 y^{3} x - 6 y^{3} (- 6 y^{3})$

Multiply $- 6$ by $4$ .

$16 x^{2} - 24 x y^{3} - 24 y^{3} x - 6 y^{3} (- 6 y^{3})$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 24 x y^{3} - 24 y^{3} x - 6 \cdot - 6 y^{3} y^{3}$

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

Move $y^{3}$ .

$16 x^{2} - 24 x y^{3} - 24 y^{3} x - 6 \cdot - 6 (y^{3} y^{3})$

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

$16 x^{2} - 24 x y^{3} - 24 y^{3} x - 6 \cdot - 6 y^{3 + 3}$

Add $3$ and $3$ .

$16 x^{2} - 24 x y^{3} - 24 y^{3} x - 6 \cdot - 6 y^{6}$

Multiply $- 6$ by $- 6$ .

$16 x^{2} - 24 x y^{3} - 24 y^{3} x + 36 y^{6}$

Subtract $24 y^{3} x$ from $- 24 x y^{3}$ .

Move $y^{3}$ .

$16 x^{2} - 24 x y^{3} - 24 x y^{3} + 36 y^{6}$

Subtract $24 x y^{3}$ from $- 24 x y^{3}$ .

$16 x^{2} - 48 x y^{3} + 36 y^{6}$

Step 4

Move $16 x^{2}$ .

$- 48 x y^{3} + 36 y^{6} + 16 x^{2}$

Step 5

Reorder $- 48 x y^{3}$ and $36 y^{6}$ .

$36 y^{6} - 48 x y^{3} + 16 x^{2}$

Simplify (4x-6y^3)^2

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