how do you factorize:
1) (x-1)^2 - (x-5)^2
2) -2x^2 -20x - 18
how do i show my workings out for them?
(x-1)^2 - (x-5)^2 = (x-1-(x-5))*(x-1+(x-5))=(x-1-x+5)*(x-1+x-5)=4(2x+4)=8(x+2)
For the second one:
assume it equals zero, find the roots and use the fact that a quadratic equation equals: a(x-x1)(x-x2), a being the constant in front of x^2 and x1 and x2 the roots.
The second equation can be written as
x^2 + 10x + 9 (dividing by -2 through out)
this can be written as (x+a)*(x+b).
Remember (x+a)*(x+b)=x^2+(a+b)*x+ab
which means x^2+(sum of a,b)*x+(Product of a,b)
For the given equation, find a and b.
Here it happens to be 1,9.
Work this out x^2 -6 x + 8
In case you're not familiar, you might want to review the rules for simple factoring (like taking the -2 out front in the second exercise), special factoring (like the difference of squares in the first exercise), and factoring quadratics (like what will be left in the second exercise, after you take the -2 out front).