Solve (y^2-3y)^2-5(y^2-3y)-50

$$( y ^ { 2 } - 3 y ) ^ { 2 } - 5 ( y ^ { 2 } - 3 y ) - 50$$

Evaluate

$$\left(y-5\right)\left(y+2\right)\left(y^{2}-3y+5\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y^{2}-3y\right)^{2}.

$$\left(y^{2}\right)^{2}-6y^{2}y+9y^{2}-5\left(y^{2}-3y\right)-50$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$y^{4}-6y^{2}y+9y^{2}-5\left(y^{2}-3y\right)-50$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y^{4}-6y^{3}+9y^{2}-5\left(y^{2}-3y\right)-50$$

Use the distributive property to multiply -5 by y^{2}-3y.

$$y^{4}-6y^{3}+9y^{2}-5y^{2}+15y-50$$

Combine 9y^{2} and -5y^{2} to get 4y^{2}.

$$y^{4}-6y^{3}+4y^{2}+15y-50$$

Expand

$$y^{4}-6y^{3}+4y^{2}+15y-50$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y^{2}-3y\right)^{2}.

$$\left(y^{2}\right)^{2}-6y^{2}y+9y^{2}-5\left(y^{2}-3y\right)-50$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$y^{4}-6y^{2}y+9y^{2}-5\left(y^{2}-3y\right)-50$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y^{4}-6y^{3}+9y^{2}-5\left(y^{2}-3y\right)-50$$

Use the distributive property to multiply -5 by y^{2}-3y.

$$y^{4}-6y^{3}+9y^{2}-5y^{2}+15y-50$$

Combine 9y^{2} and -5y^{2} to get 4y^{2}.

$$y^{4}-6y^{3}+4y^{2}+15y-50$$