Solve (b^2+5)(-b^2+7)

$$( b ^ { 2 } + 5 ) ( - b ^ { 2 } + 7 )$$

Evaluate

$$\left(7-b^{2}\right)\left(b^{2}+5\right)$$

Solution Steps

Use the distributive property to multiply b^{2}+5 by -b^{2}+7.

$$b^{2}\left(-b^{2}\right)+7b^{2}+5\left(-b^{2}\right)+35$$

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

$$b^{4}\left(-1\right)+7b^{2}+5\left(-1\right)b^{2}+35$$

Multiply 5 and -1 to get -5.

$$b^{4}\left(-1\right)+7b^{2}-5b^{2}+35$$

Combine 7b^{2} and -5b^{2} to get 2b^{2}.

$$b^{4}\left(-1\right)+2b^{2}+35$$

Expand

$$35+2b^{2}-b^{4}$$

Solution Steps

Use the distributive property to multiply b^{2}+5 by -b^{2}+7.

$$b^{2}\left(-b^{2}\right)+7b^{2}+5\left(-b^{2}\right)+35$$

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

$$b^{4}\left(-1\right)+7b^{2}+5\left(-1\right)b^{2}+35$$

Multiply 5 and -1 to get -5.

$$b^{4}\left(-1\right)+7b^{2}-5b^{2}+35$$

Combine 7b^{2} and -5b^{2} to get 2b^{2}.

$$b^{4}\left(-1\right)+2b^{2}+35$$