Solve (-y^2)*(-2y^2)-5y*(-2y^3)+3y^3*(-4y)=

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

Evaluate

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Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(-y^{2}\right)\left(-2\right)y^{2}-5y^{4}\left(-2\right)+3y^{3}\left(-4\right)y$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(-y^{2}\right)\left(-2\right)y^{2}-5y^{4}\left(-2\right)+3y^{4}\left(-4\right)$$

Multiply 5 and -2 to get -10.

$$\left(-y^{2}\right)\left(-2\right)y^{2}-\left(-10y^{4}\right)+3y^{4}\left(-4\right)$$

The opposite of -10y^{4} is 10y^{4}.

$$\left(-y^{2}\right)\left(-2\right)y^{2}+10y^{4}+3y^{4}\left(-4\right)$$

Multiply 3 and -4 to get -12.

$$\left(-y^{2}\right)\left(-2\right)y^{2}+10y^{4}-12y^{4}$$

Combine 10y^{4} and -12y^{4} to get -2y^{4}.

$$\left(-y^{2}\right)\left(-2\right)y^{2}-2y^{4}$$

Multiply -1 and -2 to get 2.

$$2y^{2}y^{2}-2y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2y^{4}-2y^{4}$$

Combine 2y^{4} and -2y^{4} to get 0.

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Factor

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Solution Steps

Factor out 2.

$$2\left(y^{2}y^{2}+5yy^{3}-6y^{3}y\right)$$

Consider y^{4}+5y^{4}-6y^{4}. Factor out y^{4}.

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