Algebra Examples

Simplify -2x^2(x-5)+x(2x^2-10x)+x
-2x2(x-5)+x(2x2-10x)+x
Step 1
Simplify each term.
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Step 1.1
Apply the distributive property.
-2x2x-2x2-5+x(2x2-10x)+x
Step 1.2
Multiply x2 by x by adding the exponents.
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Step 1.2.1
Move x.
-2(xx2)-2x2-5+x(2x2-10x)+x
Step 1.2.2
Multiply x by x2.
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Step 1.2.2.1
Raise x to the power of 1.
-2(x1x2)-2x2-5+x(2x2-10x)+x
Step 1.2.2.2
Use the power rule aman=am+n to combine exponents.
-2x1+2-2x2-5+x(2x2-10x)+x
-2x1+2-2x2-5+x(2x2-10x)+x
Step 1.2.3
Add 1 and 2.
-2x3-2x2-5+x(2x2-10x)+x
-2x3-2x2-5+x(2x2-10x)+x
Step 1.3
Multiply -5 by -2.
-2x3+10x2+x(2x2-10x)+x
Step 1.4
Apply the distributive property.
-2x3+10x2+x(2x2)+x(-10x)+x
Step 1.5
Rewrite using the commutative property of multiplication.
-2x3+10x2+2xx2+x(-10x)+x
Step 1.6
Rewrite using the commutative property of multiplication.
-2x3+10x2+2xx2-10xx+x
Step 1.7
Simplify each term.
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Step 1.7.1
Multiply x by x2 by adding the exponents.
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Step 1.7.1.1
Move x2.
-2x3+10x2+2(x2x)-10xx+x
Step 1.7.1.2
Multiply x2 by x.
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Step 1.7.1.2.1
Raise x to the power of 1.
-2x3+10x2+2(x2x1)-10xx+x
Step 1.7.1.2.2
Use the power rule aman=am+n to combine exponents.
-2x3+10x2+2x2+1-10xx+x
-2x3+10x2+2x2+1-10xx+x
Step 1.7.1.3
Add 2 and 1.
-2x3+10x2+2x3-10xx+x
-2x3+10x2+2x3-10xx+x
Step 1.7.2
Multiply x by x by adding the exponents.
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Step 1.7.2.1
Move x.
-2x3+10x2+2x3-10(xx)+x
Step 1.7.2.2
Multiply x by x.
-2x3+10x2+2x3-10x2+x
-2x3+10x2+2x3-10x2+x
-2x3+10x2+2x3-10x2+x
-2x3+10x2+2x3-10x2+x
Step 2
Simplify by adding terms.
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Step 2.1
Combine the opposite terms in -2x3+10x2+2x3-10x2+x.
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Step 2.1.1
Add -2x3 and 2x3.
10x2+0-10x2+x
Step 2.1.2
Add 10x2 and 0.
10x2-10x2+x
Step 2.1.3
Subtract 10x2 from 10x2.
0+x
0+x
Step 2.2
Add 0 and x.
x
x
-2x2(x-5)+x(2x2-10x)+x
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