Step by step solution :
Step 1 :
Equation at the end of step 1 :
((48•(x2))+(48x•(y2)))+(22•3y4)
Step 2 :
Equation at the end of step 2 :
((48 • (x2)) + (24•3xy2)) + (22•3y4)
Step 3 :
Equation at the end of step 3 :
((24•3x2) + (24•3xy2)) + (22•3y4)
Step 4 :
Step 5 :
Pulling out like terms : 5.1
Pull out like factors :
48x2 + 48xy2 + 12y4 = 12 • (4x2 + 4xy2 + y4)
Trying to factor a multi variable polynomial :
5.2 Factoring 4x2 + 4xy2 + y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (2x + y2)•(2x + y2)
Detecting a perfect square :
5.3 4x2 +4xy2 +y4 is a perfect square
It factors into (2x+y2)•(2x+y2)
which is another way of writing (2x+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
Final result :
12 • (2x + y2)2
Hope this helps!
