Replace * with a monomial so that the trinomial may be represented by a square of a binomial: 0.01b2 + * +100c2Replace * with a monomial so that the trinomial m

Question

Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial:
0.01b2 + ∗ +100c2

Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial:

0.01b² + ∗ +100c²

Answer 1

(a+b)² = a² + 2ab + b²

 

we have .01b² + x + 100c²

and need to know the calue of x so that this

is a perfect square trinomial.

 

a² = .01b

a = √(.01b²) = .1b

 

b² = 100c²

b = √(100c²) = 10c

 

2ab = 2(.1b)(10c)

      = 2bc

 

(.1b + 10c)² = .01b² + 2bc + 100c²