52y^3(72y^2-98)÷117y^2(6y-7)
Answers
Answer:
Final result :
8y5 • (6y + 7) • (6y - 7)2
——————————————————————————
9
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((23•32y2)-98)
(((52•(y3))•——————————————)•y2)•(6y-7)
117
Step 2 :
72y2 - 98
Simplify —————————
117
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
72y2 - 98 = 2 • (36y2 - 49)
Trying to factor as a Difference of Squares :
3.2 Factoring: 36y2 - 49
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 : 36 is the square of 6
Check : 49 is the square of 7
Check : y2 is the square of y1
Factorization is : (6y + 7) • (6y - 7)
Equation at the end of step 3 :
2•(6y+7)•(6y-7)
(((52•(y3))•———————————————)•y2)•(6y-7)
117
Step 4 :
Equation at the end of step 4 :
2•(6y+7)•(6y-7)
(((22•13y3)•———————————————)•y2)•(6y-7)
117
Step 5 :
Multiplying exponents :
5.1 22 multiplied by 21 = 2(2 + 1) = 23
Canceling Out :
5.2 Canceling out 13 as it appears on both sides of the fraction line
Equation at the end of step 5 :
8y3 • (6y + 7) • (6y - 7)
(————————————————————————— • y2) • (6y - 7)
9
Step 6 :
Multiplying exponential expressions :
6.1 y3 multiplied by y2 = y(3 + 2) = y5
Equation at the end of step 6 :
8y5 • (6y + 7) • (6y - 7)
————————————————————————— • (6y - 7)
9
Step 7 :
Multiplying Exponential Expressions :
7.1 Multiply (6y-7) by (6y-7)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (6y-7) and the exponents are :
1 , as (6y-7) is the same number as (6y-7)1
and 1 , as (6y-7) is the same number as (6y-7)1
The product is therefore, (6y-7)(1+1) = (6y-7)2
Final result :
8y5 • (6y + 7) • (6y - 7)2
——————————————————————————
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