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]
