Sure, let's simplify each expression by distributing the terms inside the brackets.
### (a) [tex]\( 2(x^2 + x + 1) \)[/tex]
To simplify this expression, distribute the 2 to each term inside the bracket:
[tex]\[ 2(x^2) + 2(x) + 2(1) \][/tex]
So the simplified expression is:
[tex]\[ 2x^2 + 2x + 2 \][/tex]
### (b) [tex]\( p(q + r + s) \)[/tex]
To simplify, distribute [tex]\( p \)[/tex] to each term inside the bracket:
[tex]\[ p(q) + p(r) + p(s) \][/tex]
So the simplified expression is:
[tex]\[ pq + pr + ps \][/tex]
### (c) [tex]\( -3(x + 2y + 3z) \)[/tex]
To simplify, distribute [tex]\(-3\)[/tex] to each term inside the bracket:
[tex]\[ -3(x) + (-3)(2y) + (-3)(3z) \][/tex]
This simplifies to:
[tex]\[ -3x - 6y - 9z \][/tex]
### (d) [tex]\( x(2 \times 2 + x + 7) \)[/tex]
First, simplify the expression inside the bracket:
[tex]\[ 2 \times 2 = 4 \][/tex]
So the expression becomes:
[tex]\[ x(4 + x + 7) \][/tex]
Next, distribute [tex]\( x \)[/tex] to each term inside the bracket:
[tex]\[ x(4) + x(x) + x(7) \][/tex]
This simplifies to:
[tex]\[ 4x + x^2 + 7x \][/tex]
Finally, combine the like terms:
[tex]\[ x^2 + 11x \][/tex]
So the simplified expression is:
[tex]\[ x^2 + 11x \][/tex]
Therefore, the simplified versions of the given expressions are:
- [tex]\((a)\)[/tex] [tex]\( 2x^2 + 2x + 2 \)[/tex]
- [tex]\((b)\)[/tex] [tex]\( pq + pr + ps \)[/tex]
- [tex]\((c)\)[/tex] [tex]\( -3x - 6y - 9z \)[/tex]
- [tex]\((d)\)[/tex] [tex]\( x^2 + 11x \)[/tex]
