Solve -n^2(n^2+5n+6)=

$$- n ^ { 2 } ( n ^ { 2 } + 5 n + 6 ) =$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -n^{2} by n^{2}+5n+6.

$$\left(-n^{2}\right)n^{2}+5\left(-n^{2}\right)n+6\left(-n^{2}\right)$$

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

$$-n^{4}+5\left(-1\right)n^{2}n+6\left(-1\right)n^{2}$$

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

$$-n^{4}+5\left(-1\right)n^{3}+6\left(-1\right)n^{2}$$

Multiply 5 and -1 to get -5.

$$-n^{4}-5n^{3}+6\left(-1\right)n^{2}$$

Multiply 6 and -1 to get -6.

$$-n^{4}-5n^{3}-6n^{2}$$

Expand

$$-\left(n^{4}+5n^{3}+6n^{2}\right)$$

Solution Steps

Use the distributive property to multiply -n^{2} by n^{2}+5n+6.

$$\left(-n^{2}\right)n^{2}+5\left(-n^{2}\right)n+6\left(-n^{2}\right)$$

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

$$-n^{4}+5\left(-1\right)n^{2}n+6\left(-1\right)n^{2}$$

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

$$-n^{4}+5\left(-1\right)n^{3}+6\left(-1\right)n^{2}$$

Multiply 5 and -1 to get -5.

$$-n^{4}-5n^{3}+6\left(-1\right)n^{2}$$

Multiply 6 and -1 to get -6.

$$-n^{4}-5n^{3}-6n^{2}$$