The value of p is 0.6
What is a binomial expression?
A binomial expression is an algebraic expression that contains only two terms.
Binomial expansions are used to expand exponents of two terms
The expression is given as:
[tex]px^2(5 + px)^8[/tex]
When the expression in bracket is expanded, one of its term is:
[tex]px^2(5 + px)^8 = px^2 (..........70 \times p^4 \times x^4...........)[/tex]
So, we have:
[tex]px^2(5 + px)^8 = px^2 (..........70 \times 5^4 \times (px)^4...........)[/tex]
[tex]px^2(5 + px)^8 = px^2 (..........70 \times 625 \times (px)^4...........)[/tex]
[tex]px^2(5 + px)^8 = px^2 (..........43750 (px)^4...........)[/tex]
[tex]px^2(5 + px)^8 = px^2 (..........43750 p^4x^4...........)[/tex]
Expand the bracket, to get the coefficient of x^6
[tex]px^2(5 + px)^8 = px^2 (..........43750 p^5x^6...........)[/tex]
The coefficient equals 3402.
So, we have:
[tex]43750p^5 = 3402[/tex]
Divide both sides by 43750
[tex]p^5 = 0.07776[/tex]
Take the 5th root of both sides
[tex]p = 0.6[/tex]
Hence, the value of p is 0.6
Read more about binomial expansions at:
https://brainly.com/question/13602562
