Question

factorise 1...(2+5y)^2 +2(2x+5y)(3x-5y)+(3x-5y)^2
2...25(x+y)^2-40(x+y)(x-y)+16(x-y)^2

Answer 1

Answer:

1. (2+5y)2+2(2x+5y)(3x-5y)+(3x-5y)2  

Final result :

 -20yx + 20y + 21x2 + 4

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((5y+2)2)+(2•(5y+2x)•(3x-5y)))+(3x-5y)2

Step  2  :

Equation at the end of step  2  :

 (((5y+2)2)+2•(5y+2x)•(3x-5y))+(3x-5y)2

Step  3  :

3.1     Evaluate :  (3x-5y)2   =    9x2-30yx+25y2  

Final result :

 -20yx + 20y + 21x2 + 4

Factorize from this number

2.25(x+y)2-40(x+y)(x-y)+16(x-y)2  

Final result :

 (x + 9y)2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((25•((x+y)2))-((40•(x+y))•(x-y)))+16•(x-y)2

Step  2  :

Equation at the end of step  2  :

 ((25•((x+y)2))-(40•(x+y)•(x-y)))+16•(x-y)2

Step  3  :

Equation at the end of step  3  :

 ((25•((x+y)2))-40•(x+y)•(x-y))+16•(x-y)2

Step  4  :

Equation at the end of step  4  :

 (25•(x+y)2-40•(x+y)•(x-y))+16•(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 + 18xy + 81y2  

Try to factor this multi-variable trinomial using trial and error  

Found a factorization  :  (x + 9y)•(x + 9y)

Detecting a perfect square :

5.3    x2  +18xy  +81y2  is a perfect square  

It factors into  (x+9y)•(x+9y)

which is another way of writing  (x+9y)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 + 9y)2

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