For the first part, part a, we are given that:
0.01b^2+ ∗ +100c^2
In quadratic equations we know that the middle term (the one that is missing) will be twice the square root of the first and the last terms.
Now, we know that the square root of the first term is: [tex] \sqrt{0.01b^2} =0.1b [/tex] Let us represent this by [tex] x [/tex]. Therefore, [tex] x=0.1b [/tex]
and the square root of the last term is: [tex] \sqrt{100c^2} =10c [/tex]
Let this be [tex] y [/tex]. Therefore, [tex] y=10c [/tex]
Therefore, the middle term, * is: [tex] 2xy=2\times0.1b\times 10c=2bc [/tex]
Likewise in the part b, we will have the middle term to be:
[tex] 2\times \sqrt{25a^2} \times \sqrt{\frac{1}{4}b^2} =2\times 5a\times \frac{1}{2}b=5ab [/tex]
because the first and the last terms are 25a^2 and 1/4 b^2 and we know that the middle term will be twice the square root of the first and the last terms.
