Question

Replace ∗ with a monomial so that the trinomial may be represented by a square of a binomial: b2 + 20b +*

Answer 1

Given:

The expression is:

$b^2+20b$

To find:

The a monomial so that the trinomial may be represented by a square of a binomial.

Solution:

If an expression is $x^2+bx$, then be need to add square of half of coefficient of x, i.e., $\left(\dfrac{b}{2}\right)^2$ in the given expression to make in perfect square.

We have,

$b^2+20b$

Here, coefficient of b is 20,so wee need to add square of half of coefficient of b, i.e., $\left(\dfrac{20}{2}\right)^2$.

$\left(\dfrac{20}{2}\right)^2=10^2$

$\left(\dfrac{20}{2}\right)^2=100$

Therefore, we need to add 100 to make $b^2+20b$ a perfect square binomial.