Q62. - Algebra 1

Question

Write an expression that uses exponents, at least three different operations and two sets of parentheses. Explain the steps you would take to evaluate the expression.

Step-by-Step Solution

Answer

$a^2-\left[\right(b^2+c)\cdot d]$

Step 1 –Formation of expression

Let a, b, c and d be the four values which form an expression. 

An expression having exponents, at least three different operations and two sets of parentheses is,

$a^2-\left[\right(b^2+c)\cdot d]$

Here, a and b have exponents 2. Addition, subtraction and multiplication are the three different operations and round brackets ( ), square brackets [ ] are the two sets of parentheses.

Step 2 – Example of applying BODMAS rule

The expression $b(c-d)-e$ can be written as

$\begin{array}{l}b(c-d)÷e=\left[\right(b\times c)-(b\times d\left)\right]÷e\\ =(bc-bd)÷e\\ =\frac{(bc-bd)}{e}\end{array}$

Step 3–Formation of expression

$a^2-\left[\right(b^2+c)\cdot d]$

Squaring the term within round brackets ( ) (Q BODMAS Rule)

$a^2-\left[\right(p+c)\cdot d]$ (Assume $b^2=p$)

Solving the term having round brackets ( ) within the square brackets [ ] (Q BODMAS Rule)

$a^2-[e\cdot d]$

Solving the term within square brackets [ ] (Q BODMAS Rule)

$a^2-f$ (Assume $p+c=e$)

Squaring the term a before subtracting by f (Q BODMAS Rule)

$=g-f$ (Assume $a^2=g$)

The expression having exponents, at least three different operations and two sets of parentheses: $a^2-\left[\right(b^2+c)\cdot d]$.

The evaluation of the expression $a^2-\left[\right(b^2+c)\cdot d]$ comes out to be $g-f$.