Question Video: Writing Algebraic Expressions | Nagwa Question Video: Writing Algebraic Expressions | Nagwa

# Question Video: Writing Algebraic Expressions Mathematics • First Year of Preparatory School

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Write an expression for double the square of π₯, which is then divided by 9 less than the cube of π¦.

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### Video Transcript

Write an expression for double the square of π₯, which is then divided by nine less than the cube of π¦.

In this question, we want to represent a series of operations applied to multiple given variables. When dealing with any problem of this type, it is important that we get the order of operations correct. The first part of the relationship says, βDouble the square of π₯.β We begin by squaring the variable, which we write as π₯ squared. We then need to double the expression. We note that in the order of operations, exponentiation is carried out before multiplication, so we can write this as two π₯ squared.

Now letβs consider the second part of the relationship: nine less than the cube of π¦. We need to cube π¦, written π¦ cubed. Then, we need to decrease this value by nine. Since subtraction is carried out after exponentiation, this can be written as π¦ cubed minus nine.

Finally, we need to divide the first expression by the second expression, which gives us two π₯ squared divided by π¦ cubed minus nine. It is worth noting that whilst we could put both the numerator and denominator in parentheses, this is not required, since it is convention to evaluate the numerator and the denominator of the quotient first before carrying out the division operation.

We can therefore conclude that the correct expression is two π₯ squared over π¦ cubed minus nine.

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