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Basic Math
Simplify (n-1)*(2n-1)
(n-1)⋅(2n-1)(n−1)⋅(2n−1)
Step 1
Expand (n-1)(2n-1)(n−1)(2n−1) using the FOIL Method.
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Step 1.1
Apply the distributive property.
n(2n-1)-1(2n-1)n(2n−1)−1(2n−1)
Step 1.2
Apply the distributive property.
n(2n)+n⋅-1-1(2n-1)n(2n)+n⋅−1−1(2n−1)
Step 1.3
Apply the distributive property.
n(2n)+n⋅-1-1(2n)-1⋅-1n(2n)+n⋅−1−1(2n)−1⋅−1
n(2n)+n⋅-1-1(2n)-1⋅-1n(2n)+n⋅−1−1(2n)−1⋅−1
Step 2
Simplify and combine like terms.
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Step 2.1
Simplify each term.
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Step 2.1.1
Rewrite using the commutative property of multiplication.
2n⋅n+n⋅-1-1(2n)-1⋅-12n⋅n+n⋅−1−1(2n)−1⋅−1
Step 2.1.2
Multiply nn by nn by adding the exponents.
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Step 2.1.2.1
Move nn.
2(n⋅n)+n⋅-1-1(2n)-1⋅-12(n⋅n)+n⋅−1−1(2n)−1⋅−1
Step 2.1.2.2
Multiply nn by nn.
2n2+n⋅-1-1(2n)-1⋅-12n2+n⋅−1−1(2n)−1⋅−1
2n2+n⋅-1-1(2n)-1⋅-12n2+n⋅−1−1(2n)−1⋅−1
Step 2.1.3
Move -1−1 to the left of nn.
2n2-1⋅n-1(2n)-1⋅-12n2−1⋅n−1(2n)−1⋅−1
Step 2.1.4
Rewrite -1n−1n as -n−n.
2n2-n-1(2n)-1⋅-12n2−n−1(2n)−1⋅−1
Step 2.1.5
Multiply 22 by -1−1.
2n2-n-2n-1⋅-12n2−n−2n−1⋅−1
Step 2.1.6
Multiply -1−1 by -1−1.
2n2-n-2n+12n2−n−2n+1
2n2-n-2n+12n2−n−2n+1
Step 2.2
Subtract 2n2n from -n−n.
2n2-3n+12n2−3n+1
2n2-3n+12n2−3n+1
 [x2  12  √π  ∫xdx ]  ⎡⎢⎣x2  12  √π  ∫xdx ⎤⎥⎦