Question

Ali was asked to factorise x^2y^2 + 36-4x^2-9y^2 .He tried some ways of grouping terms as shown below:
x^2y^2 + 36-4x^2-9y^2= (x^2y^2 + 36) - (4x^2+9y^2)
x^2y^2 + 36-4x^2-9y^2= (x^2y^2 + 36-4x^2)-9y^2
x^2y^2 + 36-4x^2-9y^2=x^2y^2 + (36-4x^2-9y^2)
As he could not carry out factorisation with the above groupings,he concluded that the expression could not be factorised.Do you agree with him? Why or why not?

Answer 1

2x  

2

+8x+3x+122, x, squared, plus, 8, x, plus, 3, x, plus, 12

First, notice that there is no factor common to all terms in 2x^2+8x+3x+122x  

2

+8x+3x+122, x, squared, plus, 8, x, plus, 3, x, plus, 12. However, if we group the first two terms together and the last two terms together, each group has its own GCF, or greatest common factor:

 

In particular, there is a GCF of 2x2x2, x in the first grouping and a GCF of 333 in the second grouping. We can factor these out to obtain the following expression:

2x(x+4)+3(x+4)2x(x+4)+3(x+4)