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\left(3x\right)^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Consider \left(3x+2\right)\left(3x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.
3^{2}x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Expand \left(3x\right)^{2}.
9x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4-5x\left(x-1\right)-\left(4x^{2}-4x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.
9x^{2}-4-5x\left(x-1\right)-4x^{2}+4x-1
To find the opposite of 4x^{2}-4x+1, find the opposite of each term.
9x^{2}-4-5x^{2}+5x-4x^{2}+4x-1
Use the distributive property to multiply -5x by x-1.
4x^{2}-4+5x-4x^{2}+4x-1
Combine 9x^{2} and -5x^{2} to get 4x^{2}.
-4+5x+4x-1
Combine 4x^{2} and -4x^{2} to get 0.
-4+9x-1
Combine 5x and 4x to get 9x.
-5+9x
Subtract 1 from -4 to get -5.
\left(3x\right)^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Consider \left(3x+2\right)\left(3x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.
3^{2}x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Expand \left(3x\right)^{2}.
9x^{2}-4-5x\left(x-1\right)-\left(2x-1\right)^{2}
Calculate 3 to the power of 2 and get 9.
9x^{2}-4-5x\left(x-1\right)-\left(4x^{2}-4x+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.
9x^{2}-4-5x\left(x-1\right)-4x^{2}+4x-1
To find the opposite of 4x^{2}-4x+1, find the opposite of each term.
9x^{2}-4-5x^{2}+5x-4x^{2}+4x-1
Use the distributive property to multiply -5x by x-1.
4x^{2}-4+5x-4x^{2}+4x-1
Combine 9x^{2} and -5x^{2} to get 4x^{2}.
-4+5x+4x-1
Combine 4x^{2} and -4x^{2} to get 0.
-4+9x-1
Combine 5x and 4x to get 9x.
-5+9x
Subtract 1 from -4 to get -5.