Solve (y-5)(y+5)-(y+2)(y^2-2y+4)

$$( y - 5 ) ( y + 5 ) - ( y + 2 ) ( y ^ { 2 } - 2 y + 4 )$$

Evaluate

$$-y^{3}+y^{2}-33$$

Solution Steps

Consider \left(y-5\right)\left(y+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$y^{2}-25-\left(y+2\right)\left(y^{2}-2y+4\right)$$

Use the distributive property to multiply y+2 by y^{2}-2y+4 and combine like terms.

$$y^{2}-25-\left(y^{3}+8\right)$$

To find the opposite of y^{3}+8, find the opposite of each term.

$$y^{2}-25-y^{3}-8$$

Subtract 8 from -25 to get -33.

$$y^{2}-33-y^{3}$$

Expand

$$-y^{3}+y^{2}-33$$

Solution Steps

Consider \left(y-5\right)\left(y+5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 5.

$$y^{2}-25-\left(y+2\right)\left(y^{2}-2y+4\right)$$

Use the distributive property to multiply y+2 by y^{2}-2y+4 and combine like terms.

$$y^{2}-25-\left(y^{3}+8\right)$$

To find the opposite of y^{3}+8, find the opposite of each term.

$$y^{2}-25-y^{3}-8$$

Subtract 8 from -25 to get -33.

$$y^{2}-33-y^{3}$$