Answer:
a) (x/2 +3)^2
b) (5a -3b)^2
c) (x/3 +y/5)^2
d) (10b -3c)^2
e) (a/4 -2b)^2
Step-by-step explanation:
Assuming you can do that, write the terms of the quadratic in lexicographical order. (The square terms will be first and last.) Then the binomial is the "sum" of the square roots of the first and last terms with the sign of the middle term.
Using (e) as an example, the term are already in order. (In (d), they need to be rearranged.) The first term is 1/16a^2, and its square root is 1/4a = a/4. The last term is 4b^2 and its square root is 2b. The sign of the middle term is negative, so these two roots will be separated by a minus sign:
(a/4 - 2b)^2
The expression you want is the square of the binomial.
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As a check, you can make sure that double the product of these terms is the middle term of the trinomial you started with.
In this example, that double product is 2·a/4·(-2b) = -ab, which exactly matches the middle term you started with.
