Algebraic Expressions

a) If [tex]\( l = 6 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( h = 2 \)[/tex], evaluate the following expressions:

(i) [tex]\( l \times b \)[/tex]

(ii) [tex]\( l \times b \times h \)[/tex]

(iii) [tex]\( 2(l + b) \)[/tex]

(iv) [tex]\( 2h(l + b) \)[/tex]

(v) [tex]\( l^2 \)[/tex]

b) If [tex]\( x = 2 \)[/tex] and [tex]\( y = 3 \)[/tex], evaluate the following expression:

(vi) [tex]\( 6l^2 \)[/tex]



Answer :

Sure, let's evaluate each expression step-by-step given the values [tex]\( l = 6 \)[/tex], [tex]\( b = 4 \)[/tex], [tex]\( h = 2 \)[/tex], [tex]\( x = 2 \)[/tex], and [tex]\( y = 3 \)[/tex].

### Expression (i): [tex]\( 1 \times b \)[/tex]

Here, we multiply 1 with the value of [tex]\( b \)[/tex].

[tex]\[ 1 \times b = 1 \times 4 = 4 \][/tex]

So, the result of expression (i) is [tex]\( 4 \)[/tex].

### Expression (iv): [tex]\( 2h(l + b) \)[/tex]

First, we find the sum inside the parentheses.

[tex]\[ l + b = 6 + 4 = 10 \][/tex]

Now, we multiply by [tex]\( h \)[/tex] which is 2, and then by 2.

[tex]\[ 2h(l + b) = 2 \times 2 \times 10 = 4 \times 10 = 40 \][/tex]

So, the result of expression (iv) is [tex]\( 40 \)[/tex].

### Expression (ii): [tex]\( l \times b \times h \)[/tex]

We multiply [tex]\( l \)[/tex], [tex]\( b \)[/tex], and [tex]\( h \)[/tex] together.

[tex]\[ l \times b \times h = 6 \times 4 \times 2 = 24 \times 2 = 48 \][/tex]

So, the result of expression (ii) is [tex]\( 48 \)[/tex].

### Expression (v): [tex]\( l^2 \)[/tex]

We square the value of [tex]\( l \)[/tex].

[tex]\[ l^2 = 6^2 = 36 \][/tex]

So, the result of expression (v) is [tex]\( 36 \)[/tex].

### Expression (iii): [tex]\( 2(1 + b) \)[/tex]

First, we add 1 to [tex]\( b \)[/tex].

[tex]\[ 1 + b = 1 + 4 = 5 \][/tex]

Now we multiply by 2.

[tex]\[ 2(1 + b) = 2 \times 5 = 10 \][/tex]

So, the result of expression (iii) is [tex]\( 10 \)[/tex].

### Expression (vi): [tex]\( 6 l^2 \)[/tex]

First, we square the value of [tex]\( l \)[/tex] and then multiply by 6.

[tex]\[ l^2 = 6^2 = 36 \][/tex]

Now, we multiply by 6.

[tex]\[ 6 l^2 = 6 \times 36 = 216 \][/tex]

So, the result of expression (vi) is [tex]\( 216 \)[/tex].

Thus, the evaluated results for the given expressions are:
[tex]\[ \begin{aligned} \text{(i)} & \quad 4, \\ \text{(ii)} & \quad 48, \\ \text{(iii)} & \quad 10, \\ \text{(iv)} & \quad 40, \\ \text{(v)} & \quad 36, \\ \text{(vi)} & \quad 216. \end{aligned} \][/tex]