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2. For each expression, write an equivalent expression without brackets.

(a) [tex]2(x + 2 + x + 1)[/tex]

(b) [tex]p(q + r + s)[/tex]

(c) [tex]-3(x + 2y + 3z)[/tex]

(d) [tex]x(2 \times 2 + x + 7)[/tex]



Answer :

GinnyAnswer
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]

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