Answers 1
Answer:
Solution
= 12
m= -6
m
Step-by-step explanation:
Step 1
Use binomial theorem (a - b)² =
a² - 2ab + b² to expand (m - 3)².
| m² 6m +9=81
Step 2
—
Subtract 81 from both sides.
m² - 6m +9 - 81 =
0
Step 3
Subtract 81 from 9 to get -72.
| m² − 6m – 72 = 0Step 4
To solve the equation, factor
m² – 6m – 72 using formula
m² + (a+b) m + ab =
(m+a) (m+b). To find a and b,
set up a system to be solved.
| a+b=-6 ab = -72
Step 5
Since ab is negative, a and b
have the opposite signs. Since
a + b is negative, the negative
number has greater absolute
value than the positive. List all
such integer pairs that give
product -72.
| 1, −72 2, −36 3,–244, −18 6, -12 8, –9
Step 6
Calculate the sum for each pair.
1 – 72 = −71 2 –
-
36=-34 3− 24 =
-214-18 = -14
6-12-68-9=
| −1
Step 7
The solution is the pair that gives
sum -6.
| a=-12 b=6
Step 8
Rewrite factored expression
(m+a) (m+b) using the
obtained values.
| (m
(m – 12) (m+6)
Step 9
To find equation solutions, solve
m - 12 = 0 and m+ 6 = 0.
m = 12 m =-6
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