Simplify 6x^2y^4(5x^2-3x^2y^2+4y^2)

$6 x^{2} y^{4} (5 x^{2} - 3 x^{2} y^{2} + 4 y^{2})$

Step 1

Apply the distributive property.

$6 x^{2} y^{4} (5 x^{2}) + 6 x^{2} y^{4} (- 3 x^{2} y^{2}) + 6 x^{2} y^{4} (4 y^{2})$

Step 2

Simplify.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

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

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

Add $2$ and $4$ .

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

Step 3

Simplify each term.

Multiply $5$ by $6$ .

$30 x^{4} y^{4} + 6 x^{4} y^{4} (- 3 y^{2}) + 6 x^{2} y^{6} \cdot 4$

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$30 x^{4} y^{4} + 6 x^{4} (y^{2} y^{4}) \cdot - 3 + 6 x^{2} y^{6} \cdot 4$

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

$30 x^{4} y^{4} + 6 x^{4} y^{2 + 4} \cdot - 3 + 6 x^{2} y^{6} \cdot 4$

Add $2$ and $4$ .

$30 x^{4} y^{4} + 6 x^{4} y^{6} \cdot - 3 + 6 x^{2} y^{6} \cdot 4$

Multiply $- 3$ by $6$ .

$30 x^{4} y^{4} - 18 x^{4} y^{6} + 6 x^{2} y^{6} \cdot 4$

Multiply $4$ by $6$ .

$30 x^{4} y^{4} - 18 x^{4} y^{6} + 24 x^{2} y^{6}$