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x^{2}-\left(2y^{2}\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}-2^{2}\left(y^{2}\right)^{2}
Expand \left(2y^{2}\right)^{2}.
x^{2}-2^{2}y^{4}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
x^{2}-4y^{4}
Calculate 2 to the power of 2 and get 4.
x^{2}-\left(2y^{2}\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x^{2}-2^{2}\left(y^{2}\right)^{2}
Expand \left(2y^{2}\right)^{2}.
x^{2}-2^{2}y^{4}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
x^{2}-4y^{4}
Calculate 2 to the power of 2 and get 4.