( 2 x - 1 ) ( 2 x + 1 ) - ( x - 5 ) ( 4 x + 3
Evaluate
17x+14
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17x+14
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\left(2x\right)^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Expand \left(2x\right)^{2}.
4x^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Calculate 2 to the power of 2 and get 4.
4x^{2}-1-\left(x-5\right)\left(4x+3\right)
Calculate 1 to the power of 2 and get 1.
4x^{2}-1-\left(4x^{2}+3x-20x-15\right)
Apply the distributive property by multiplying each term of x-5 by each term of 4x+3.
4x^{2}-1-\left(4x^{2}-17x-15\right)
Combine 3x and -20x to get -17x.
4x^{2}-1-4x^{2}-\left(-17x\right)-\left(-15\right)
To find the opposite of 4x^{2}-17x-15, find the opposite of each term.
4x^{2}-1-4x^{2}+17x-\left(-15\right)
The opposite of -17x is 17x.
4x^{2}-1-4x^{2}+17x+15
The opposite of -15 is 15.
-1+17x+15
Combine 4x^{2} and -4x^{2} to get 0.
14+17x
Add -1 and 15 to get 14.
\left(2x\right)^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Consider \left(2x-1\right)\left(2x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2^{2}x^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Expand \left(2x\right)^{2}.
4x^{2}-1^{2}-\left(x-5\right)\left(4x+3\right)
Calculate 2 to the power of 2 and get 4.
4x^{2}-1-\left(x-5\right)\left(4x+3\right)
Calculate 1 to the power of 2 and get 1.
4x^{2}-1-\left(4x^{2}+3x-20x-15\right)
Apply the distributive property by multiplying each term of x-5 by each term of 4x+3.
4x^{2}-1-\left(4x^{2}-17x-15\right)
Combine 3x and -20x to get -17x.
4x^{2}-1-4x^{2}-\left(-17x\right)-\left(-15\right)
To find the opposite of 4x^{2}-17x-15, find the opposite of each term.
4x^{2}-1-4x^{2}+17x-\left(-15\right)
The opposite of -17x is 17x.
4x^{2}-1-4x^{2}+17x+15
The opposite of -15 is 15.
-1+17x+15
Combine 4x^{2} and -4x^{2} to get 0.
14+17x
Add -1 and 15 to get 14.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}