Solve (2k+k^2)*(-k^2+2k)

$$( 2 k + k ^ { 2 } ) \cdot ( - k ^ { 2 } + 2 k )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 2k+k^{2} by -k^{2}+2k.

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

Multiply 2 and -1 to get -2.

$$-2kk^{2}+4k^{2}+k^{2}\left(-1\right)k^{2}+2k^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-2k^{3}+4k^{2}+k^{2}\left(-1\right)k^{2}+2k^{3}$$

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

$$-2k^{3}+4k^{2}+k^{4}\left(-1\right)+2k^{3}$$

Combine -2k^{3} and 2k^{3} to get 0.

$$4k^{2}+k^{4}\left(-1\right)$$

Expand

$$4k^{2}-k^{4}$$

Solution Steps

Use the distributive property to multiply 2k+k^{2} by -k^{2}+2k.

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

Multiply 2 and -1 to get -2.

$$-2kk^{2}+4k^{2}+k^{2}\left(-1\right)k^{2}+2k^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-2k^{3}+4k^{2}+k^{2}\left(-1\right)k^{2}+2k^{3}$$

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

$$-2k^{3}+4k^{2}+k^{4}\left(-1\right)+2k^{3}$$

Combine -2k^{3} and 2k^{3} to get 0.

$$4k^{2}+k^{4}\left(-1\right)$$