Simplify (4y^3-0.5y^2)^2

${(4 y^{3} - 0.5 y^{2})}^{2}$

Step 1

Rewrite ${(4 y^{3} - 0.5 y^{2})}^{2}$ as $(4 y^{3} - 0.5 y^{2}) (4 y^{3} - 0.5 y^{2})$ .

$(4 y^{3} - 0.5 y^{2}) (4 y^{3} - 0.5 y^{2})$

Step 2

Expand $(4 y^{3} - 0.5 y^{2}) (4 y^{3} - 0.5 y^{2})$ using the FOIL Method.

Apply the distributive property.

$4 y^{3} (4 y^{3} - 0.5 y^{2}) - 0.5 y^{2} (4 y^{3} - 0.5 y^{2})$

Apply the distributive property.

$4 y^{3} (4 y^{3}) + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3} - 0.5 y^{2})$

Apply the distributive property.

$4 y^{3} (4 y^{3}) + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 y^{3} y^{3} + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

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

Move $y^{3}$ .

$4 \cdot 4 (y^{3} y^{3}) + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

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

$4 \cdot 4 y^{3 + 3} + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Add $3$ and $3$ .

$4 \cdot 4 y^{6} + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Multiply $4$ by $4$ .

$16 y^{6} + 4 y^{3} (- 0.5 y^{2}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Rewrite using the commutative property of multiplication.

$16 y^{6} + 4 \cdot - 0.5 y^{3} y^{2} - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$16 y^{6} + 4 \cdot - 0.5 (y^{2} y^{3}) - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

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

$16 y^{6} + 4 \cdot - 0.5 y^{2 + 3} - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Add $2$ and $3$ .

$16 y^{6} + 4 \cdot - 0.5 y^{5} - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Multiply $4$ by $- 0.5$ .

$16 y^{6} - 2 y^{5} - 0.5 y^{2} (4 y^{3}) - 0.5 y^{2} (- 0.5 y^{2})$

Rewrite using the commutative property of multiplication.

$16 y^{6} - 2 y^{5} - 0.5 \cdot 4 y^{2} y^{3} - 0.5 y^{2} (- 0.5 y^{2})$

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$16 y^{6} - 2 y^{5} - 0.5 \cdot 4 (y^{3} y^{2}) - 0.5 y^{2} (- 0.5 y^{2})$

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

$16 y^{6} - 2 y^{5} - 0.5 \cdot 4 y^{3 + 2} - 0.5 y^{2} (- 0.5 y^{2})$

Add $3$ and $2$ .

$16 y^{6} - 2 y^{5} - 0.5 \cdot 4 y^{5} - 0.5 y^{2} (- 0.5 y^{2})$

Multiply $- 0.5$ by $4$ .

$16 y^{6} - 2 y^{5} - 2 y^{5} - 0.5 y^{2} (- 0.5 y^{2})$

Rewrite using the commutative property of multiplication.

$16 y^{6} - 2 y^{5} - 2 y^{5} - 0.5 \cdot - 0.5 y^{2} y^{2}$

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

Move $y^{2}$ .

$16 y^{6} - 2 y^{5} - 2 y^{5} - 0.5 \cdot - 0.5 (y^{2} y^{2})$

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

$16 y^{6} - 2 y^{5} - 2 y^{5} - 0.5 \cdot - 0.5 y^{2 + 2}$

Add $2$ and $2$ .

$16 y^{6} - 2 y^{5} - 2 y^{5} - 0.5 \cdot - 0.5 y^{4}$

Multiply $- 0.5$ by $- 0.5$ .

$16 y^{6} - 2 y^{5} - 2 y^{5} + 0.25 y^{4}$

Subtract $2 y^{5}$ from $- 2 y^{5}$ .

$16 y^{6} - 4 y^{5} + 0.25 y^{4}$

Simplify (4y^3-0.5y^2)^2

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