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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5y-2y^{2}\right)^{2}.

$$y^{2}-5y+25y^{2}-20yy^{2}+4\left(y^{2}\right)^{2}$$

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

$$y^{2}-5y+25y^{2}-20y^{3}+4\left(y^{2}\right)^{2}$$

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

$$y^{2}-5y+25y^{2}-20y^{3}+4y^{4}$$

Combine y^{2} and 25y^{2} to get 26y^{2}.

$$26y^{2}-5y-20y^{3}+4y^{4}$$

Expand

$$4y^{4}-20y^{3}+26y^{2}-5y$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5y-2y^{2}\right)^{2}.

$$y^{2}-5y+25y^{2}-20yy^{2}+4\left(y^{2}\right)^{2}$$

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

$$y^{2}-5y+25y^{2}-20y^{3}+4\left(y^{2}\right)^{2}$$

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

$$y^{2}-5y+25y^{2}-20y^{3}+4y^{4}$$

Combine y^{2} and 25y^{2} to get 26y^{2}.

$$26y^{2}-5y-20y^{3}+4y^{4}$$