divide 16x^2y-48xy^2+8x^2y√2 by 8x√2y^2
Answers
Answer:
STEP1:Equation at the end of step 1
((16 • (x4)) - (23x2 • y2)) + y4
STEP 2 :
Equation at the end of step2:
(24x4 - 23x2y2) + y4
STEP3:Trying to factor a multi variable polynomial
3.1 Factoring 16x4 - 8x2y2 + y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (4x2 - y2)•(4x2 - y2)
Detecting a perfect square :
3.2 16x4 -8x2y2 +y4 is a perfect square
It factors into (4x2-y2)•(4x2-y2)
which is another way of writing (4x2-y2)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Trying to factor as a Difference of Squares:
3.3 Factoring: 4x2-y2
Put the exponent aside, try to factor 4x2-y2
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 : 4 is the square of 2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (2x + y) • (2x - y)
Raise to the exponent which was put aside
Factorization becomes : (2x + y)2 • (2x - y)2
Final result :
(2x + y)2 • (2x - y)2