Basic Math Examples

Simplify ((3m)/(6m+18))(m^2-7m-30)
(3m6m+18)(m2-7m-30)(3m6m+18)(m27m30)
Step 1
Factor 66 out of 6m+186m+18.
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Step 1.1
Factor 66 out of 6m6m.
3m6(m)+18(m2-7m-30)3m6(m)+18(m27m30)
Step 1.2
Factor 66 out of 1818.
3m6m+63(m2-7m-30)3m6m+63(m27m30)
Step 1.3
Factor 66 out of 6m+636m+63.
3m6(m+3)(m2-7m-30)3m6(m+3)(m27m30)
3m6(m+3)(m2-7m-30)3m6(m+3)(m27m30)
Step 2
Cancel the common factor of 33 and 66.
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Step 2.1
Factor 33 out of 3m3m.
3(m)6(m+3)(m2-7m-30)3(m)6(m+3)(m27m30)
Step 2.2
Cancel the common factors.
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Step 2.2.1
Factor 33 out of 6(m+3)6(m+3).
3(m)3(2(m+3))(m2-7m-30)3(m)3(2(m+3))(m27m30)
Step 2.2.2
Cancel the common factor.
3m3(2(m+3))(m2-7m-30)3m3(2(m+3))(m27m30)
Step 2.2.3
Rewrite the expression.
m2(m+3)(m2-7m-30)m2(m+3)(m27m30)
m2(m+3)(m2-7m-30)m2(m+3)(m27m30)
m2(m+3)(m2-7m-30)m2(m+3)(m27m30)
Step 3
Multiply m2(m+3)m2(m+3) by m2-7m-30m27m30.
m(m2-7m-30)2(m+3)m(m27m30)2(m+3)
Step 4
Factor m2-7m-30m27m30 using the AC method.
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Step 4.1
Consider the form x2+bx+cx2+bx+c. Find a pair of integers whose product is cc and whose sum is bb. In this case, whose product is -3030 and whose sum is -77.
-10,310,3
Step 4.2
Write the factored form using these integers.
m((m-10)(m+3))2(m+3)m((m10)(m+3))2(m+3)
m(m-10)(m+3)2(m+3)m(m10)(m+3)2(m+3)
Step 5
Cancel the common factor of m+3m+3.
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Step 5.1
Cancel the common factor.
m(m-10)(m+3)2(m+3)m(m10)(m+3)2(m+3)
Step 5.2
Rewrite the expression.
m(m-10)2m(m10)2
m(m-10)2m(m10)2
 [x2  12  π  xdx ]  x2  12  π  xdx