Part (a):
Before we begin, remember the difference between squares rule which is as follows:
a² - b² = (a+b)(a-b)
Now, for the given we have:
1 - r⁴
This can be rewritten as:
(1)² - (r²)²
We can apply the difference between squares as follows:
(1-r²)(1+r²)
Now, checking the result we reached, we can note that we can apply the difference between squares again on the first bracket.
Doing this, we will reach:
(1-r)(1+r)(1+r²) .............> This is the simplest factored form
Part (b):
The given expression is:
6x² + 7x - 49
This is a polynomial of second degree.
This means that we can use the quadratic formula to get the solutions. The quadratic formula is shown in the attached image
From the expression, we can note that:
a = 6
b = 7
c = -49
Substituting in the formula, we would find that:
either x = 7/3 ...........> This means that the first bracket is (3x-7)
or x = -7/2 .............> This means that the second bracket is (2x+7)
Based on the above, the simplest factored form of 6x² + 7x - 49 is:
(3x-7)(2x+7)
Hope this helps :)