find the lcm of 15a^2b(a^2-b^2) and 40ab^2(a^2-b^2)
Answers
Slope = -1.200/2.000 = -0.600
a-intercept = 0/3 = 0.00000
b-intercept = 0/5 = 0.00000
Slope = 1
a-intercept = 0/1 = 0.00000
b-intercept = 0/-1 = -0.00000
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 3 more similar replacement(s).
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
10*a*b-15*b^2/4*a^2-6*a*b-(10*b^2-15*a*b/4*a*b-6*a^2)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(b2) b
((10ab-((15•————)•(a2)))-6ab)-(((10•(b2))-(((15a•—)•a)•b))-(2•3a2)) = 0
4 4
Step 2 :
b
Simplify —
4
Equation at the end of step 2 :
(b2) b
((10ab-((15•————)•(a2)))-6ab)-(((10•(b2))-(((15a•—)•a)•b))-(2•3a2)) = 0
4 4
Step 3 :
Equation at the end of step 3 :
(b2) 15a2b2
((10ab-((15•————)•(a2)))-6ab)-(((2•5b2)-——————)-(2•3a2)) = 0
4 4
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
(2•5b2) (2•5b2) • 4
(2•5b2) = ——————— = ———————————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(2•5b2) • 4 - (15a2b2) 40b2 - 15a2b2
—————————————————————— = —————————————
4 4
Equation at the end of step 4 :
(b2) (40b2-15a2b2)
((10ab-((15•————)•(a2)))-6ab)-(—————————————-(2•3a2)) = 0
4 4
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 4 as the denominator :
(2•3a2) (2•3a2) • 4
(2•3a2) = ——————— = ———————————
1 4
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
40b2 - 15a2b2 = -5b2 • (3a2 - 8)
Trying to factor as a Difference of Squares :
6.2 Factoring: 3a2 - 8
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Adding fractions that have a common denominator :
6.3 Adding up the two equivalent fractions
-5b2 • (3a2-8) - ((2•3a2) • 4) -15a2b2 - 24a2 + 40b2
—————————————————————————————— = —————————————————————
4 4
Equation at the end of step 6 :
(b2) (-15a2b2-24a2+40b2)
((10ab-((15•————)•(a2)))-6ab)-——————————————————— = 0
4 4
Step 7 :
b2
Simplify ——
4
Equation at the end of step 7 :
b2 (-15a2b2-24a2+40b2)
((10ab-((15•——)•a2))-6ab)-——————————————————— = 0
4 4
Step 8 :
Answer:
Refers to the attachment
