5.8k views
4 votes
Replace ∗ with a monomial so that the derived expression may be represented as a square of a binomial: * +14b+49

User Bmavity
by
6.4k points

1 Answer

4 votes

Answer:

* = b²

Explanation:

You know that the square of a binomial is of the form ...

(x + y)² = x² + 2xy + y²

Matching given terms, we have ...

49 = y²

2xy = 14b

Solving the first of these relations for y, we have

y = √49 = 7

Putting that in the second relation and solving for x, we find ...

2x·7 = 14b

14x = 14b

x = b

Then the first term of the expansion, x², will be .

The missing term is b².

User Genzer
by
6.8k points