3. 16x4 - 72x2y2 + 81y4
use the identity and factorize
Answers
Answer:
((16•(x4))-((72•(x2))•(y2)))+34y4
STEP
2
:
Equation at the end of step
2
:
((16 • (x4)) - ((23•32x2) • y2)) + 34y4
STEP
3
:
Equation at the end of step
3
:
(24x4 - (23•32x2y2)) + 34y4
STEP
4
:
Trying to factor a multi variable polynomial
4.1 Factoring 16x4 - 72x2y2 + 81y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (4x2 - 9y2)•(4x2 - 9y2)
Detecting a perfect square :
4.2 16x4 -72x2y2 +81y4 is a perfect square
It factors into (4x2-9y2)•(4x2-9y2)
which is another way of writing (4x2-9y2)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:
4.3 Factoring: 4x2-9y2
Put the exponent aside, try to factor 4x2-9y2
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 : 9 is the square of 3
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (2x + 3y) • (2x - 3y)
Raise to the exponent which was put aside
Factorization becomes : (2x + 3y)2 • (2x - 3y)2
Step-by-step explanation: