solve 0.09x^2-0.25y^2
Answers
Answer:
3x + 5y) • (3x - 5y)
—————————————————————
100
Steps:
(9/100)x2-(25/100)y2
Final result :
(3x + 5y) • (3x - 5y)
—————————————————————
100
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "0.25" was replaced by "(25/100)". 2 more similar replacement(s)
Step by step solution :
Step 1 :
1
Simplify —
4
Equation at the end of step 1 :
9 1
(——— • (x2)) - (— • y2)
100 4
Step 2 :
Equation at the end of step 2 :
9 y2
(——— • (x2)) - ——
100 4
Step 3 :
9
Simplify ———
100
Equation at the end of step 3 :
9 y2
(——— • x2) - ——
100 4
Step 4 :
Equation at the end of step 4 :
9x2 y2
——— - ——
100 4
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 100
The right denominator is : 4
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 2 2
5 2 0 2
Product of all
Prime Factors 100 4 100
Least Common Multiple:
100
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 25
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 9x2
—————————————————— = ———
L.C.M 100
R. Mult. • R. Num. y2 • 25
—————————————————— = ———————
L.C.M 100
Adding fractions that have a common denominator :
5.4 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:
9x2 - (y2 • 25) 9x2 - 25y2
——————————————— = ——————————
100 100
Trying to factor as a Difference of Squares :
5.5 Factoring: 9x2 - 25y2
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 : 9 is the square of 3
Check : 25 is the square of 5
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (3x + 5y) • (3x - 5y)
Final result :
(3x + 5y) • (3x - 5y)
—————————————————————
100
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