Question

[Maximum mark: 6]

Answer 1

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:

$px^2(5 + px)^8$

When the expression in bracket is expanded, one of its term is:

$px^2(5 + px)^8 = px^2 (..........70 \times p^4 \times x^4...........)$

So, we have:

$px^2(5 + px)^8 = px^2 (..........70 \times 5^4 \times (px)^4...........)$

$px^2(5 + px)^8 = px^2 (..........70 \times 625 \times (px)^4...........)$

$px^2(5 + px)^8 = px^2 (..........43750 (px)^4...........)$

$px^2(5 + px)^8 = px^2 (..........43750 p^4x^4...........)$

Expand the bracket, to get the coefficient of x^6

$px^2(5 + px)^8 = px^2 (..........43750 p^5x^6...........)$

The coefficient equals 3402.

So, we have:

$43750p^5 = 3402$

Divide both sides by 43750

$p^5 = 0.07776$

Take the 5th root of both sides

$p = 0.6$

Hence, the value of p is 0.6

Read more about binomial expansions at:

brainly.com/question/13602562