Evaluate
45\left(x^{4}-y^{4}\right)
Expand
45x^{4}-45y^{4}
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49\left(x^{2}\right)^{2}+28x^{2}y^{2}+4\left(y^{2}\right)^{2}-\left(2x^{2}+7y^{2}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7x^{2}+2y^{2}\right)^{2}.
49x^{4}+28x^{2}y^{2}+4\left(y^{2}\right)^{2}-\left(2x^{2}+7y^{2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(2x^{2}+7y^{2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4\left(x^{2}\right)^{2}+28x^{2}y^{2}+49\left(y^{2}\right)^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x^{2}+7y^{2}\right)^{2}.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4x^{4}+28x^{2}y^{2}+49\left(y^{2}\right)^{2}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4x^{4}+28x^{2}y^{2}+49y^{4}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-4x^{4}-28x^{2}y^{2}-49y^{4}
To find the opposite of 4x^{4}+28x^{2}y^{2}+49y^{4}, find the opposite of each term.
45x^{4}+28x^{2}y^{2}+4y^{4}-28x^{2}y^{2}-49y^{4}
Combine 49x^{4} and -4x^{4} to get 45x^{4}.
45x^{4}+4y^{4}-49y^{4}
Combine 28x^{2}y^{2} and -28x^{2}y^{2} to get 0.
45x^{4}-45y^{4}
Combine 4y^{4} and -49y^{4} to get -45y^{4}.
49\left(x^{2}\right)^{2}+28x^{2}y^{2}+4\left(y^{2}\right)^{2}-\left(2x^{2}+7y^{2}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7x^{2}+2y^{2}\right)^{2}.
49x^{4}+28x^{2}y^{2}+4\left(y^{2}\right)^{2}-\left(2x^{2}+7y^{2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(2x^{2}+7y^{2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4\left(x^{2}\right)^{2}+28x^{2}y^{2}+49\left(y^{2}\right)^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x^{2}+7y^{2}\right)^{2}.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4x^{4}+28x^{2}y^{2}+49\left(y^{2}\right)^{2}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-\left(4x^{4}+28x^{2}y^{2}+49y^{4}\right)
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
49x^{4}+28x^{2}y^{2}+4y^{4}-4x^{4}-28x^{2}y^{2}-49y^{4}
To find the opposite of 4x^{4}+28x^{2}y^{2}+49y^{4}, find the opposite of each term.
45x^{4}+28x^{2}y^{2}+4y^{4}-28x^{2}y^{2}-49y^{4}
Combine 49x^{4} and -4x^{4} to get 45x^{4}.
45x^{4}+4y^{4}-49y^{4}
Combine 28x^{2}y^{2} and -28x^{2}y^{2} to get 0.
45x^{4}-45y^{4}
Combine 4y^{4} and -49y^{4} to get -45y^{4}.
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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