Answer:
The value which is needed to be added to transform the quadratic expression
as a perfect square trinomial is 16.
Step-by-step explanation:
A quadratic expression is an expression in which the highest power of the variable is 2 or it can be said that the degree of the expression is 2.
The identity for
is given as follows:
![(a+b)^{2}=a^{2}+b^{2}+2\times(a)\times(b)](https://tex.z-dn.net/?f=%28a%2Bb%29%5E%7B2%7D%3Da%5E%7B2%7D%2Bb%5E%7B2%7D%2B2%5Ctimes%28a%29%5Ctimes%28b%29)
<u>Step 1: </u>
Break down the given polynomial
.
<u>Step 2: </u>
Now compare the polynomial with the above indentity.
On comparing it is observed that the value of a is x and the value of b is 4.
<u>Step 3: </u>
In order to make the polynomial
a perfect square, add
to the broked down polynomial because on comparing the above polynomials the value of b is 4 and the square of 4 is 16.
<u>Step 4:</u>
Now as per the identity
the polynomial
is written as follows:
.
Therefore, the perfect square for the given polynomial is
which is created by adding 16 to the given expression.
Learn more:
- A problem to obtain the y-intercept of a quadratic function brainly.com/question/1332667
- A problem to obtain the binomial and trinomial brainly.com/question/1394854
Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Quadratic expression
Keywords: Quadratic, quadratic expression, polynomial, quadratic polynomial, perfect square, trinomial, degree, highest power, transform, identities, break down, perfect square, middle term split, x^2+8x,methamatics, algebra.