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Using factorization, the expression x² + 6x + 9 = ?
- a)(x + 3)(x - 3)
- b)(x + 1)(x + 2)
- c)(x + 3) (x + 3)
- d)(x + 2) (x + 2)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Using factorization, the expression x + 6x + 9 = ?a)(x + 3)(x - 3)b)(x...
x^2 + 6x + 9
x^2 + 3x + 3x + 9
x (x + 3 ) + 3 (x + 3)
(x + 3) (x + 3 )
(x + 3 )^2
Most Upvoted Answer
Using factorization, the expression x + 6x + 9 = ?a)(x + 3)(x - 3)b)(x...
Factorization of the expression x^2 - 6x + 9
To factorize the given expression x^2 - 6x + 9, we need to find two binomials whose product equals the given expression.
Step 1: Identify the factors of the constant term
The constant term in the expression is 9. We need to find two numbers whose product is 9 and whose sum is the coefficient of the linear term, which is -6.
The factors of 9 are:
1 x 9 = 9
-1 x -9 = 9
3 x 3 = 9
Step 2: Determine the two binomials
We need to find two binomials in the form (x + a)(x + b) such that the product of the binomials is equal to the given expression x^2 - 6x + 9.
From the factors of 9, we can see that 3 and 3 satisfy the condition. Therefore, the two binomials are (x + 3)(x + 3), which can also be written as (x + 3)^2.
Step 3: Verify the factorization
To verify the factorization, we can expand the expression (x + 3)(x + 3) using the distributive property:
(x + 3)(x + 3) = x(x + 3) + 3(x + 3)
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9
The expanded form of the expression matches the given expression x^2 - 6x + 9. Therefore, the factorization is correct.
Conclusion:
The expression x^2 - 6x + 9 can be factorized as (x + 3)(x + 3) or (x + 3)^2. Therefore, the correct answer is option C.
To factorize the given expression x^2 - 6x + 9, we need to find two binomials whose product equals the given expression.
Step 1: Identify the factors of the constant term
The constant term in the expression is 9. We need to find two numbers whose product is 9 and whose sum is the coefficient of the linear term, which is -6.
The factors of 9 are:
1 x 9 = 9
-1 x -9 = 9
3 x 3 = 9
Step 2: Determine the two binomials
We need to find two binomials in the form (x + a)(x + b) such that the product of the binomials is equal to the given expression x^2 - 6x + 9.
From the factors of 9, we can see that 3 and 3 satisfy the condition. Therefore, the two binomials are (x + 3)(x + 3), which can also be written as (x + 3)^2.
Step 3: Verify the factorization
To verify the factorization, we can expand the expression (x + 3)(x + 3) using the distributive property:
(x + 3)(x + 3) = x(x + 3) + 3(x + 3)
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9
The expanded form of the expression matches the given expression x^2 - 6x + 9. Therefore, the factorization is correct.
Conclusion:
The expression x^2 - 6x + 9 can be factorized as (x + 3)(x + 3) or (x + 3)^2. Therefore, the correct answer is option C.
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Using factorization, the expression x + 6x + 9 = ?a)(x + 3)(x - 3)b)(x + 1)(x + 2)c)(x + 3) (x + 3)d)(x + 2) (x + 2)Correct answer is option 'C'. Can you explain this answer?
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