Expand and simplify: (x - 5y) (x + 3y)
1 answer:
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Answer:
Step-by-step explanation:
Given
Required
Solve
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
<em>The numbers in parentheses are carried from previous sum</em>
Start from the right
Write 0, carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0 0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0 0 0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0 0 0 0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0 0 0 0 0
Write 0 carry 1
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
0 0 0 0 0 0 0
Write 6
2 4 5 6 7 3 8 9
+ 3 5 4 3 2 6 1 1
----------------------------
6 0 0 0 0 0 0 0
Hence:
Answer:
there are no extraneous solutions to the equation
Step-by-step explanation:
Given
= x + 2 ( square both sides )
8x + 9 = (x + 2)² ← expand
8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )
0 = x² - 4x - 5 ← in standard form
0 = (x - 5)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 5 : =
= 7
right side = 5 + 2 = 7
left side = right side ⇒ x = 5 is a solution
x = - 1 : =
= 1
right side = - 1 + 2 = 1
left side = right side ⇒ x = - 1 is a solution
There are no extraneous solutions
This is very easy!! I have attached a picture I have drawn if you are a visual learner... well, everything else like computations is here.
.
This is the PYTHAGOREAN THEOREM!!
.
If you don't know, it says that the lengths of the legs squared added together all equal the hypotenuse squared in a right triangle!!
.
And if you want to know why the "triangle" has a right angle... well, are towers slanted? I mean, other than the Leaning Tower of Pizza. I mean Pisa.
.
So... we plug it in!!
.
Formula: a^2 + b^2 = c^2.
.
Plug it in: 11^2+ 61^2 = c^2
.
c^2 = 3842.
.
So now what?
.
SQUARE ROOT OF EVERYTHING!!
.
c = <span>√3842.
.
So? c = approximately 61.984.
.
Hope I helped!!</span>
.
This is the PYTHAGOREAN THEOREM!!
.
If you don't know, it says that the lengths of the legs squared added together all equal the hypotenuse squared in a right triangle!!
.
And if you want to know why the "triangle" has a right angle... well, are towers slanted? I mean, other than the Leaning Tower of Pizza. I mean Pisa.
.
So... we plug it in!!
.
Formula: a^2 + b^2 = c^2.
.
Plug it in: 11^2+ 61^2 = c^2
.
c^2 = 3842.
.
So now what?
.
SQUARE ROOT OF EVERYTHING!!
.
c = <span>√3842.
.
So? c = approximately 61.984.
.
Hope I helped!!</span>