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From the following, which are the factors of a2 - b + ab - a?
- a)(a−1)and (a−b)
- b)(a+b)and (a−1)
- c)(a+1)and (a−b)
- d)(a+b) and (a+1)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
From the following, which are the factors ofa2- b + ab - a?a)(a−...
Understanding the Expression
To factor the expression a^2 - b + ab - a, we start by rearranging the terms for clarity:
- a^2 + ab - a - b
Grouping Terms
Next, we can group the terms to facilitate factoring:
- (a^2 - a) + (ab - b)
Factoring Each Group
Now, we can factor out common factors from each group:
- From the first group (a^2 - a), we can factor out 'a':
- a(a - 1)
- From the second group (ab - b), we factor out 'b':
- b(a - 1)
Now, we rewrite the expression combining both factors:
- a(a - 1) + b(a - 1)
Factoring Out the Common Binomial
Since both terms share a common factor of (a - 1), we can factor it out:
- (a - 1)(a + b)
Identifying the Correct Answer
Now, let's analyze the options provided:
- a) (a - 1) and (a - b)
- b) (a + b) and (a - 1)
- c) (a + 1) and (a - b)
- d) (a + b) and (a + 1)
From our factoring, we see that the expression can be represented as:
- (a - 1)(a + b)
Thus, the correct factors are indeed:
- Option B: (a + b) and (a - 1)
This confirms that option B is the correct answer, as it matches the factors we derived from the expression.
To factor the expression a^2 - b + ab - a, we start by rearranging the terms for clarity:
- a^2 + ab - a - b
Grouping Terms
Next, we can group the terms to facilitate factoring:
- (a^2 - a) + (ab - b)
Factoring Each Group
Now, we can factor out common factors from each group:
- From the first group (a^2 - a), we can factor out 'a':
- a(a - 1)
- From the second group (ab - b), we factor out 'b':
- b(a - 1)
Now, we rewrite the expression combining both factors:
- a(a - 1) + b(a - 1)
Factoring Out the Common Binomial
Since both terms share a common factor of (a - 1), we can factor it out:
- (a - 1)(a + b)
Identifying the Correct Answer
Now, let's analyze the options provided:
- a) (a - 1) and (a - b)
- b) (a + b) and (a - 1)
- c) (a + 1) and (a - b)
- d) (a + b) and (a + 1)
From our factoring, we see that the expression can be represented as:
- (a - 1)(a + b)
Thus, the correct factors are indeed:
- Option B: (a + b) and (a - 1)
This confirms that option B is the correct answer, as it matches the factors we derived from the expression.
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Community Answer
From the following, which are the factors ofa2- b + ab - a?a)(a−...
a² - b + ab - a = a² + ab - b - a
= ( a² + ab ) - ( b + a )
= a ( a + b) - (a + b )
= ( a + b) ( a - 1 )
= ( a² + ab ) - ( b + a )
= a ( a + b) - (a + b )
= ( a + b) ( a - 1 )
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