Solve 4(4x^2-8)-[5(2x^2-1)+9]=

$$4 ( 4 x ^ { 2 } - 8 ) - [ 5 ( 2 x ^ { 2 } - 1 ) + 9 ] =$$

Evaluate

$$6\left(x^{2}-6\right)$$

Solution Steps

Use the distributive property to multiply 4 by 4x^{2}-8.

$$16x^{2}-32-\left(5\left(2x^{2}-1\right)+9\right)$$

Use the distributive property to multiply 5 by 2x^{2}-1.

$$16x^{2}-32-\left(10x^{2}-5+9\right)$$

Add -5 and 9 to get 4.

$$16x^{2}-32-\left(10x^{2}+4\right)$$

To find the opposite of 10x^{2}+4, find the opposite of each term.

$$16x^{2}-32-10x^{2}-4$$

Combine 16x^{2} and -10x^{2} to get 6x^{2}.

$$6x^{2}-32-4$$

Subtract 4 from -32 to get -36.

$$6x^{2}-36$$

Expand

$$6x^{2}-36$$

Solution Steps

Use the distributive property to multiply 4 by 4x^{2}-8.

$$16x^{2}-32-\left(5\left(2x^{2}-1\right)+9\right)$$

Use the distributive property to multiply 5 by 2x^{2}-1.

$$16x^{2}-32-\left(10x^{2}-5+9\right)$$

Add -5 and 9 to get 4.

$$16x^{2}-32-\left(10x^{2}+4\right)$$

To find the opposite of 10x^{2}+4, find the opposite of each term.

$$16x^{2}-32-10x^{2}-4$$

Combine 16x^{2} and -10x^{2} to get 6x^{2}.

$$6x^{2}-32-4$$

Subtract 4 from -32 to get -36.

$$6x^{2}-36$$