Question

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

Answer 1

Answer:

Below in bold.

Step-by-step explanation:

The identity is of the form

(a + b)^2 = a^2 + 2ab + b^2.

a) Sqrt 49 = 7 and we need + 28 as the middle coefficient . We get this with

2*7 + 2*7 so the first coefficient is 2*2 = 4.

So * = 4a^2.

(2a + 7)^2 = (2a + 7)(2a + 7) = 4x^2 + 14a + 14a + 49.

b) -6 * -6 = 36   -24 =  2*-6 + 2 *-6 so the last term is 4x^2

c) The middle term  must be an 'ab' term.

sqrt 6.25 = 2.5 and sqrt 1/4 = 1/2

So the coefficient of the middle term is 2.5 * 1/2 + 2.5 * 1/2

= 2.5

So the middle term is 2.5ab.

d) The first term will be in b^2.

100 = 10* 10 and we need 2 as a middle term so coefficient of the first term

will be  1/100 or 0.01.  as the 2 comes from 0.1 * 10 + 0.01 * 10 and (0.1)^2 = 0.01

So it is 0.01b^2.