Answer:
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Step by Step Solution
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Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
STEP
1
:
Simplify —
4
Equation at the end of step
(9 • (x2)) - —
2
32x2 - —
3
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
32x2 32x2 • 4
32x2 = ———— = ————————
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 :
3.2 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:
32x2 • 4 - (1) 36x2 - 1
—————————————— = ————————
4 4
Trying to factor as a Difference of Squares:
3.3 Factoring: 36x2 - 1
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 : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (6x + 1) • (6x - 1)
Final result :
(6x + 1) • (6x - 1)
———————————————————
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Answers & Comments
Answer:
1 solution(s) found
See steps
Step by Step Solution
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
STEP
1
:
1
Simplify —
4
Equation at the end of step
1
:
1
(9 • (x2)) - —
4
STEP
2
:
Equation at the end of step
2
:
1
32x2 - —
4
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 4 as the denominator :
32x2 32x2 • 4
32x2 = ———— = ————————
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 :
3.2 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:
32x2 • 4 - (1) 36x2 - 1
—————————————— = ————————
4 4
Trying to factor as a Difference of Squares:
3.3 Factoring: 36x2 - 1
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 : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (6x + 1) • (6x - 1)
Final result :
(6x + 1) • (6x - 1)
———————————————————
4