Solve -b^4(8b^2+10b-1)

$$- b ^ { 4 } ( 8 b ^ { 2 } + 10 b - 1 )$$

Evaluate

$$\left(1-10b-8b^{2}\right)b^{4}$$

Solution Steps

Use the distributive property to multiply -b^{4} by 8b^{2}+10b-1.

$$8\left(-b^{4}\right)b^{2}+10\left(-b^{4}\right)b-\left(-b^{4}\right)$$

Multiply -1 and -1 to get 1.

$$8\left(-b^{4}\right)b^{2}+10\left(-b^{4}\right)b+b^{4}$$

Multiply 8 and -1 to get -8.

$$-8b^{4}b^{2}+10\left(-1\right)b^{4}b+b^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8b^{6}+10\left(-1\right)b^{4}b+b^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-8b^{6}+10\left(-1\right)b^{5}+b^{4}$$

Multiply 10 and -1 to get -10.

$$-8b^{6}-10b^{5}+b^{4}$$

Expand

$$b^{4}-10b^{5}-8b^{6}$$

Solution Steps

Use the distributive property to multiply -b^{4} by 8b^{2}+10b-1.

$$8\left(-b^{4}\right)b^{2}+10\left(-b^{4}\right)b-\left(-b^{4}\right)$$

Multiply -1 and -1 to get 1.

$$8\left(-b^{4}\right)b^{2}+10\left(-b^{4}\right)b+b^{4}$$

Multiply 8 and -1 to get -8.

$$-8b^{4}b^{2}+10\left(-1\right)b^{4}b+b^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8b^{6}+10\left(-1\right)b^{4}b+b^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-8b^{6}+10\left(-1\right)b^{5}+b^{4}$$

Multiply 10 and -1 to get -10.

$$-8b^{6}-10b^{5}+b^{4}$$