Question

what algebraic expression corresponds to the statement: ¨The cube of half of the sum of any two numbers¨?

Answer 1

Hello!

Cube = x³

The sum of any two numbers = x + y

Half = ÷2

So the algebraic expression is going to be $(\frac{x+y}{2} )^{3}$

    Hope it helps! :))

Answer 2

Answer:

The algebraic expression representing the statement 'The cube of half of the sum of any two numbers' = = $\frac{x^3}{8} +\frac{y^3}{8} + \frac{3x^2y}{8} +\frac{3xy^2}{8}$

Step-by-step explanation:

Required to find,

An algebraic expression representing the statement 'The cube of half of the sum of any two numbers'

Solution:

'x' and 'y' be the numbers

Sum of the two numbers = x+y

Half of the sum of the two numbers = $\frac{x+y}{2}$

The cube of the half of the sum of the two numbers = $(\frac{x+y}{2})^3$

$(\frac{x+y}{2})^3 = \frac{1}{8}$[x³ +y³ + 3x²y+3xy²]

= $\frac{x^3}{8} +\frac{y^3}{8} + \frac{3x^2y}{8} +\frac{3xy^2}{8}$

∴The algebraic expression representing the statement 'The cube of half of the sum of any two numbers' = = $\frac{x^3}{8} +\frac{y^3}{8} + \frac{3x^2y}{8} +\frac{3xy^2}{8}$

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