9a whole square - 4whole square/9awhole square -16 + 24a please answer fast step by step please
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Answer:
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Explanation:
STEP
1
:
x2
Simplify ——
2
Equation at the end of step
1
:
35 x2
(((2•(a2))-9a)-(——•x))•((((9•——)•a2)-3a)-20)
12 2
STEP
2
:
Equation at the end of step 2
35 9a2x2
(((2•(a2))-9a)-(——•x))•((—————-3a)-20)
12 2
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
3a 3a • 2
3a = —— = ——————
1 2
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:
9a2x2 - (3a • 2) 9a2x2 - 6a
———————————————— = ——————————
2 2
Equation at the end of step
3
:
35 (9a2x2-6a)
(((2•(a2))-9a)-(——•x))•(——————————-20)
12 2
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 2 as the denominator :
20 20 • 2
20 = —— = ——————
1 2
STEP
5
:
Pulling out like terms :
5.1 Pull out like factors :
9a2x2 - 6a = 3a • (3ax2 - 2)
Trying to factor as a Difference of Squares:
5.2 Factoring: 3ax2 - 2
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 :
5.3 Adding up the two equivalent fractions
3a • (3ax2-2) - (20 • 2) 9a2x2 - 6a - 40
———————————————————————— = ———————————————
2 2
Equation at the end of step
5
:
35 (9a2x2-6a-40)
(((2•(a2))-9a)-(——•x))•—————————————
12 2
STEP
6
:
35
Simplify ——
12
Equation at the end of step
6
:
35 (9a2x2-6a-40)
(((2•(a2))-9a)-(——•x))•—————————————
12 2
STEP
7
:
Equation at the end of step
7
:
35x (9a2x2 - 6a - 40)
((2a2 - 9a) - ———) • —————————————————
12 2
STEP
8
:
Rewriting the whole as an Equivalent Fraction :
8.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 12 as the denominator :
2a2 - 9a (2a2 - 9a) • 12
2a2 - 9a = ———————— = ———————————————
1 12
STEP
9
:
Pulling out like terms :
9.1 Pull out like factors :
2a2 - 9a = a • (2a - 9)
Adding fractions that have a common denominator :
9.2 Adding up the two equivalent fractions
a • (2a-9) • 12 - (35x) 24a2 - 108a - 35x
——————————————————————— = —————————————————
12 12
Equation at the end of step
9
:
(24a2 - 108a - 35x) (9a2x2 - 6a - 40)
——————————————————— • —————————————————
12 2
STEP
10
:
Trying to factor a multi variable polynomial :
10.1 Factoring 24a2 - 108a - 35x
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Trying to factor a multi variable polynomial :
10.2 Factoring 9a2x2 - 6a - 40