factorise: 0.6r-0.8qr-12.8q²r
Answers
steps
Step by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "q2" was replaced by "q^2".
(2): "12.8" was replaced by "(128/10)". 3 more similar replacement(s)
STEP
1
:
64
Simplify ——
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Equation at the end of step
1
:
6 8 64
((——•r)-((——•q)•r))-((——•q2)•r)
10 10 5
STEP
2
:
Equation at the end of step 2
6 8 64q2
((——•r)-((——•q)•r))-(————•r)
10 10 5
STEP
3
:
4
Simplify —
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Equation at the end of step
3
:
6 4 64rq2
((——•r)-((—•q)•r))-—————
10 5 5
STEP
4
:
3
Simplify —
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Equation at the end of step
4
:
3 4rq 64rq2
((— • r) - ———) - —————
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STEP
5
:
Adding fractions which have a common denominator
5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3r - (4rq) 3r - 4rq
—————————— = ————————
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Equation at the end of step
5
:
(3r - 4rq) 64rq2
—————————— - —————
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STEP
6
:
STEP
7
:
Pulling out like terms
7.1 Pull out like factors :
3r - 4rq = -r • (4q - 3)
Adding fractions which have a common denominator :
7.2 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-r • (4q-3) - (64rq2) -64rq2 - 4rq + 3r
————————————————————— = —————————————————
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STEP
8
:
Pulling out like terms
8.1 Pull out like factors :
-64rq2 - 4rq + 3r = -r • (64q2 + 4q - 3)
Trying to factor by splitting the middle term
8.2 Factoring 64q2 + 4q - 3
The first term is, 64q2 its coefficient is 64 .
The middle term is, +4q its coefficient is 4 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 64 • -3 = -192
Step-2 : Find two factors of -192 whose sum equals the coefficient of the middle term, which is 4 .
-192 + 1 = -191
-96 + 2 = -94
-64 + 3 = -61
-48 + 4 = -44
-32 + 6 = -26
-24 + 8 = -16
-16 + 12 = -4
-12 + 16 = 4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 16
64q2 - 12q + 16q - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
4q • (16q-3)
Add up the last 2 terms, pulling out common factors :
1 • (16q-3)
Step-5 : Add up the four terms of step 4 :
(4q+1) • (16q-3)
Which is the desired factorization
Final result :
-r • (16q - 3) • (4q + 1)
—————————————————————————
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