The factors of (2x - 3y)^2 + 2(2x + 3y)(x+y)(x+y)^2 is?
Answers
Answer:
STEP
1
:
Equation at the end of step 1
((2x-(3•(y2)))3)+((2x-(3y2))2)
STEP
2
:
Equation at the end of step
2
:
((2x - (3y2))3) + (2x - 3y2)2
STEP
3
:
Pulling out like terms
3.1 Pull out (2x-3y2)2
After pulling out, we are left with :
(2x-3y2)2 • ( (2x-3y2) - (-1) ))
Trying to factor as a Difference of Squares:
3.2 Factoring: 2x-3y2
Put the exponent aside, try to factor 2x-3y2
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 : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Trying to factor a multi variable polynomial :
3.3 Factoring 2x - 3y2 + 1
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(2x - 3y2)2 • (2x - 3y2 + 1)
(3x - 2y), (3x - 2y)
The factors of (2x - 3y)² + 2 (2x - 3y) (x + y) + (x + y)² are (3x - 2y) and (3x - 2y).
Given data (question corrected):
The expression (2x - 3y)² + 2 (2x - 3y) (x + y) + (x + y)²
To find:
The factors of the given expression
Tips for the solution:
Algebraic identities,
a² + 2ab + b² = (a + b)² = (a + b) (a + b)
a² - 2ab + b² = (a - b)² = (a - b) (a - b)
Step-by-step explanation:
Let 2x - 3y = a and x + y = b
Then, (2x - 3y)² + 2 (2x - 3y) (x + y) + (x + y)²
= a² + 2ab + b²
= (a + b)²
= (2x - 3y + x + y)², putting the values of a and b
= (3x - 2y)²
= (3x - 2y) (3x - 2y)
∴ the required factors are (3x - 2y) and (3x - 2y).
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