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4x^{2}-6y^{2}
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4x^{2}-6y^{2}
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\left(3x\right)^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Consider \left(3x+4y\right)\left(3x-4y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
3^{2}x^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Expand \left(3x\right)^{2}.
9x^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4^{2}y^{2}-5x^{2}+10y^{2}
Expand \left(4y\right)^{2}.
9x^{2}-16y^{2}-5x^{2}+10y^{2}
Calculate 4 to the power of 2 and get 16.
4x^{2}-16y^{2}+10y^{2}
Combine 9x^{2} and -5x^{2} to get 4x^{2}.
4x^{2}-6y^{2}
Combine -16y^{2} and 10y^{2} to get -6y^{2}.
\left(3x\right)^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Consider \left(3x+4y\right)\left(3x-4y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
3^{2}x^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Expand \left(3x\right)^{2}.
9x^{2}-\left(4y\right)^{2}-5x^{2}+10y^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4^{2}y^{2}-5x^{2}+10y^{2}
Expand \left(4y\right)^{2}.
9x^{2}-16y^{2}-5x^{2}+10y^{2}
Calculate 4 to the power of 2 and get 16.
4x^{2}-16y^{2}+10y^{2}
Combine 9x^{2} and -5x^{2} to get 4x^{2}.
4x^{2}-6y^{2}
Combine -16y^{2} and 10y^{2} to get -6y^{2}.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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