Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Let's solve each part step by step:
### Part (a)
Simplify the expression: [tex]\( 4m + ((6m - 3n) - (9n - 5m) + (8m - 2n)) \)[/tex]
1. Distribute and simplify within the inner parentheses:
[tex]\[ (6m - 3n) - (9n - 5m) + (8m - 2n) \][/tex]
Rewrite subtraction as addition of negative terms:
[tex]\[ = (6m - 3n) + (-9n + 5m) + (8m - 2n) \][/tex]
2. Combine the like terms:
[tex]\[ = 6m + 5m + 8m - 3n - 9n - 2n \][/tex]
Add the 'm' terms together and the 'n' terms together:
[tex]\[ = (6m + 5m + 8m) + (-3n - 9n - 2n) \][/tex]
[tex]\[ = 19m - 14n \][/tex]
3. Now include the term from outside the parentheses:
[tex]\[ 4m + 19m - 14n \][/tex]
Combine the 'm' terms:
[tex]\[ 23m - 14n \][/tex]
The simplified expression is:
[tex]\[ 23m - 14n \][/tex]
### Part (b)
Simplify the expression: [tex]\( 2a - \{7a - (3a - 7b) + (10a - 9b)\} \)[/tex]
1. Simplify the expression within the curly braces:
[tex]\[ 7a - (3a - 7b) + (10a - 9b) \][/tex]
Distribute and simplify inside the parentheses:
[tex]\[ = 7a - 3a + 7b + 10a - 9b \][/tex]
Combine the like terms:
[tex]\[ = (7a - 3a + 10a) + (7b - 9b) \][/tex]
[tex]\[ = 14a - 2b \][/tex]
2. Now include the term from outside the curly braces:
[tex]\[ 2a - (14a - 2b) \][/tex]
Distribute the negative sign:
[tex]\[ = 2a - 14a + 2b \][/tex]
Combine the 'a' terms:
[tex]\[ = -12a + 2b \][/tex]
The simplified expression is:
[tex]\[ -12a + 2b \][/tex]
### Part (c)
Simplify the expression: [tex]\[ -(-6x + 3y - (8x - [2y - 4x - 26xy + 10x] - 9y) + 12x) \][/tex]
1. Simplify within the square brackets first:
[tex]\[ 2y - 4x - 26xy + 10x \][/tex]
Combine the 'x' terms:
[tex]\[ = 2y + (10x - 4x) - 26xy \][/tex]
[tex]\[ = 2y + 6x - 26xy \][/tex]
2. Substitute back into the inner parentheses:
[tex]\[ -6x + 3y - (8x - (2y + 6x - 26xy) - 9y) + 12x \][/tex]
Distribute and simplify within the inner parentheses:
[tex]\[ = -6x + 3y - (8x - 2y - 6x + 26xy - 9y) + 12x \][/tex]
[tex]\[ = -6x + 3y - (2x - 11y + 26xy) + 12x \][/tex]
Distribute the negative sign:
[tex]\[ = -6x + 3y - 2x + 11y - 26xy + 12x \][/tex]
Combine the like terms:
[tex]\[ = (-6x - 2x + 12x) + (3y + 11y) - 26xy \][/tex]
[tex]\[ = 4x + 14y - 26xy \][/tex]
3. Distribute the outer negative sign:
[tex]\[ = -(4x + 14y - 26xy) \][/tex]
[tex]\[ = -4x - 14y + 26xy \][/tex]
The simplified expression is:
[tex]\[ -4x - 14y + 26xy \][/tex]
### Part (a)
Simplify the expression: [tex]\( 4m + ((6m - 3n) - (9n - 5m) + (8m - 2n)) \)[/tex]
1. Distribute and simplify within the inner parentheses:
[tex]\[ (6m - 3n) - (9n - 5m) + (8m - 2n) \][/tex]
Rewrite subtraction as addition of negative terms:
[tex]\[ = (6m - 3n) + (-9n + 5m) + (8m - 2n) \][/tex]
2. Combine the like terms:
[tex]\[ = 6m + 5m + 8m - 3n - 9n - 2n \][/tex]
Add the 'm' terms together and the 'n' terms together:
[tex]\[ = (6m + 5m + 8m) + (-3n - 9n - 2n) \][/tex]
[tex]\[ = 19m - 14n \][/tex]
3. Now include the term from outside the parentheses:
[tex]\[ 4m + 19m - 14n \][/tex]
Combine the 'm' terms:
[tex]\[ 23m - 14n \][/tex]
The simplified expression is:
[tex]\[ 23m - 14n \][/tex]
### Part (b)
Simplify the expression: [tex]\( 2a - \{7a - (3a - 7b) + (10a - 9b)\} \)[/tex]
1. Simplify the expression within the curly braces:
[tex]\[ 7a - (3a - 7b) + (10a - 9b) \][/tex]
Distribute and simplify inside the parentheses:
[tex]\[ = 7a - 3a + 7b + 10a - 9b \][/tex]
Combine the like terms:
[tex]\[ = (7a - 3a + 10a) + (7b - 9b) \][/tex]
[tex]\[ = 14a - 2b \][/tex]
2. Now include the term from outside the curly braces:
[tex]\[ 2a - (14a - 2b) \][/tex]
Distribute the negative sign:
[tex]\[ = 2a - 14a + 2b \][/tex]
Combine the 'a' terms:
[tex]\[ = -12a + 2b \][/tex]
The simplified expression is:
[tex]\[ -12a + 2b \][/tex]
### Part (c)
Simplify the expression: [tex]\[ -(-6x + 3y - (8x - [2y - 4x - 26xy + 10x] - 9y) + 12x) \][/tex]
1. Simplify within the square brackets first:
[tex]\[ 2y - 4x - 26xy + 10x \][/tex]
Combine the 'x' terms:
[tex]\[ = 2y + (10x - 4x) - 26xy \][/tex]
[tex]\[ = 2y + 6x - 26xy \][/tex]
2. Substitute back into the inner parentheses:
[tex]\[ -6x + 3y - (8x - (2y + 6x - 26xy) - 9y) + 12x \][/tex]
Distribute and simplify within the inner parentheses:
[tex]\[ = -6x + 3y - (8x - 2y - 6x + 26xy - 9y) + 12x \][/tex]
[tex]\[ = -6x + 3y - (2x - 11y + 26xy) + 12x \][/tex]
Distribute the negative sign:
[tex]\[ = -6x + 3y - 2x + 11y - 26xy + 12x \][/tex]
Combine the like terms:
[tex]\[ = (-6x - 2x + 12x) + (3y + 11y) - 26xy \][/tex]
[tex]\[ = 4x + 14y - 26xy \][/tex]
3. Distribute the outer negative sign:
[tex]\[ = -(4x + 14y - 26xy) \][/tex]
[tex]\[ = -4x - 14y + 26xy \][/tex]
The simplified expression is:
[tex]\[ -4x - 14y + 26xy \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
