Solve y(y-3)-(y+7)(y-7)

$$y ( y - 3 ) - ( y + 7 ) ( y - 7 )$$

Evaluate

$$49-3y$$

Solution Steps

Use the distributive property to multiply y by y-3.

$$y^{2}-3y-\left(y+7\right)\left(y-7\right)$$

Consider \left(y+7\right)\left(y-7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$y^{2}-3y-\left(y^{2}-7^{2}\right)$$

Calculate 7 to the power of 2 and get 49.

$$y^{2}-3y-\left(y^{2}-49\right)$$

To find the opposite of y^{2}-49, find the opposite of each term.

$$y^{2}-3y-y^{2}-\left(-49\right)$$

The opposite of -49 is 49.

$$y^{2}-3y-y^{2}+49$$

Combine y^{2} and -y^{2} to get 0.

$$-3y+49$$

Expand

$$49-3y$$

Solution Steps

Use the distributive property to multiply y by y-3.

$$y^{2}-3y-\left(y+7\right)\left(y-7\right)$$

Consider \left(y+7\right)\left(y-7\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$y^{2}-3y-\left(y^{2}-7^{2}\right)$$

Calculate 7 to the power of 2 and get 49.

$$y^{2}-3y-\left(y^{2}-49\right)$$

To find the opposite of y^{2}-49, find the opposite of each term.

$$y^{2}-3y-y^{2}-\left(-49\right)$$

The opposite of -49 is 49.

$$y^{2}-3y-y^{2}+49$$

Combine y^{2} and -y^{2} to get 0.

$$-3y+49$$