Factorize:
4(x-y)²-12(x-y)(x+y)+9(x+y)²
Answers
Answer:
Step-by-step explanation:
Result:- (x + 5y)2
Equation at the end of step 1 : ((4•((x-y)2))-((12•(x-y))•(x+y)))+9•(x+y)2 Step 2 :Equation at the end of step 2 : ((4•((x-y)2))-(12•(x-y)•(x+y)))+9•(x+y)2 Step 3 :Equation at the end of step 3 : ((4•((x-y)2))-12•(x-y)•(x+y))+9•(x+y)2 Step 4 :Equation at the end of step 4 : (4•(x-y)2-12•(x-y)•(x+y))+9•(x+y)2 Step 5 : 5.1 Evaluate : (x+y)2 = x2+2xy+y2 Trying to factor a multi variable polynomial :
5.2 Factoring x2 + 10xy + 25y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (x + 5y)•(x + 5y)
Detecting a perfect square :
5.3 x2 +10xy +25y2 is a perfect square
It factors into (x+5y)•(x+5y)
which is another way of writing (x+5y)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 : (x + 5y)2
Answer:
4(x-y)² - 12(x-y)(x+y) + 9(x+y)²
= 4(x² -2xy + y²) - 12(x² - y²) + 9(x² + 2xy + y²)
= 4x² - 8xy + 4y² - 12x² + 12y² + 9x² + 18xy + 9y².
= 17x² + 10xy + 25y²
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