Solve -x^2(5x^2-x+2)

$$- x ^ { 2 } ( 5 x ^ { 2 } - x + 2 )$$

Evaluate

$$x^{2}\left(-5x^{2}+x-2\right)$$

Solution Steps

Use the distributive property to multiply -x^{2} by 5x^{2}-x+2.

$$5\left(-x^{2}\right)x^{2}-\left(-x^{2}\right)x+2\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$5\left(-x^{2}\right)x^{2}+x^{2}x+2\left(-x^{2}\right)$$

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

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

Multiply 5 and -1 to get -5.

$$-5x^{2}x^{2}+x^{3}+2\left(-1\right)x^{2}$$

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

$$-5x^{4}+x^{3}+2\left(-1\right)x^{2}$$

Multiply 2 and -1 to get -2.

$$-5x^{4}+x^{3}-2x^{2}$$

Expand

$$-5x^{4}+x^{3}-2x^{2}$$

Solution Steps

Use the distributive property to multiply -x^{2} by 5x^{2}-x+2.

$$5\left(-x^{2}\right)x^{2}-\left(-x^{2}\right)x+2\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$5\left(-x^{2}\right)x^{2}+x^{2}x+2\left(-x^{2}\right)$$

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

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

Multiply 5 and -1 to get -5.

$$-5x^{2}x^{2}+x^{3}+2\left(-1\right)x^{2}$$

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

$$-5x^{4}+x^{3}+2\left(-1\right)x^{2}$$

Multiply 2 and -1 to get -2.

$$-5x^{4}+x^{3}-2x^{2}$$