Solve 5y^{2}-(-4y^{2}+5y^2)+(y^2+9y^2-15)^2)

$$5 y ^ { 2 } - ( - 4 y ^ { 2 } + 5 y ^ { 2 } ) + ( y ^ { 2 } + 9 y ^ { 2 } - 15 ) ^ { 2 } )$$

Evaluate

$$100y^{4}-296y^{2}+225$$

Solution Steps

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

$$5y^{2}-y^{2}+\left(y^{2}+9y^{2}-15\right)^{2}$$

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

$$4y^{2}+\left(y^{2}+9y^{2}-15\right)^{2}$$

Combine y^{2} and 9y^{2} to get 10y^{2}.

$$4y^{2}+\left(10y^{2}-15\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10y^{2}-15\right)^{2}.

$$4y^{2}+100\left(y^{2}\right)^{2}-300y^{2}+225$$

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

$$4y^{2}+100y^{4}-300y^{2}+225$$

Combine 4y^{2} and -300y^{2} to get -296y^{2}.

$$-296y^{2}+100y^{4}+225$$

Expand

$$100y^{4}-296y^{2}+225$$

Solution Steps

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

$$5y^{2}-y^{2}+\left(y^{2}+9y^{2}-15\right)^{2}$$

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

$$4y^{2}+\left(y^{2}+9y^{2}-15\right)^{2}$$

Combine y^{2} and 9y^{2} to get 10y^{2}.

$$4y^{2}+\left(10y^{2}-15\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(10y^{2}-15\right)^{2}.

$$4y^{2}+100\left(y^{2}\right)^{2}-300y^{2}+225$$

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

$$4y^{2}+100y^{4}-300y^{2}+225$$

Combine 4y^{2} and -300y^{2} to get -296y^{2}.

$$-296y^{2}+100y^{4}+225$$