Question

Find the value of $(0.8x + 0.3y)(0.64{x^2} - 0.24xy + 0.09{y^2})$
A) ${(0.8x + 0.3y)^2}$
B) ${(0.8x + 0.3y)^3}$
C) ${(0.8x)^3} + {(0.3y)^3}$
D) ${(0.8x)^3} - {(0.3y)^3}$

Answer 1

Hint: Before you evaluate an algebraic expression, you need to simplify it. This will make all your calculations much easier. Here are the basic steps to follow to simplify an algebraic expression:
* remove parentheses by multiplying factors
* use exponent rules to remove parentheses in terms with exponents
* combine like terms by adding coefficients
* combine the constants

Complete step-by-step answer:
$(0.8x + 0.3y)(0.64{x^2} - 0.24xy + 0.09{y^2})$
When simplifying an expression, the first thing to look for is whether you can clear any parentheses. Often, you can use the distributive property to clear parentheses, by multiplying the factors times the terms inside the parentheses. In this expression, we can use the distributive property to get rid of the first two sets of parentheses.
$ = 0.8x(0.64{x^2} - 0.24xy + 0.09{y^2}) + 0.3y(0.64{x^2} - 0.24xy + 0.09{y^2})$
Now we can get rid of the parentheses in the term with the exponents by using the exponent rules. When a term with an exponent is raised to a power, we multiply the exponents, so $x$$(x^2)$ becomes $x^3$.
$ = 0.512{x^3} - 0.192{x^2}y + 0.072x{y^2} + 0.192{x^2}y - 0.072x{y^2} + 0.027{y^3}$
The next step in simplifying is to look for the like terms and combine them. The terms $ - 0.192{x^2}y$ and $0.072x{y^2}$have like terms with $ - 0.192{x^2}y$ and $0.072x{y^2}$, because they have the same variable raised to the same power.
$ = 0.512{x^3} + 0.027{y^3}$
As 0.512 and 0.027 are perfect cubes so we can write them as
$ = {\left( {0.8x} \right)^3} + {\left( {0.3y} \right)^3}$

So, option (C) is the correct answer.

Note: To multiply a polynomial by a monomial, apply the distributive property and then simplify each of the resulting terms.
To multiply polynomials, multiply each term in the first polynomial with each term in the second polynomial. Then combine like terms.
The product of a n -term polynomial and a m -term polynomial results in a m×n term polynomial before like terms are combined.