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Can you explain the answer of this question below:
Factorise: 4y2−12y+ 9
- A:(7y− 5)2
- B:(5y− 3)2
- C:(2y− 5)2
- D:(2y− 3)2
The answer is D.
Most Upvoted Answer
Can you explain the answer of this question below:Factorise: 4y2&minus...
We have 4y2 - 12y+9. comparing the equation with (a-b)2=a2-2ab+b2,gives us a2=(2y)2,2ab=2*3*2y and b2=(3)2.Hence the answer is (2y-3)2.
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Can you explain the answer of this question below:Factorise: 4y2&minus...
Understanding the Expression
To factorise the quadratic expression 4y² - 12y + 9, we need to identify the coefficients and apply the factorisation techniques.
Step 1: Identify Coefficients
- The given expression is in the form of ax² + bx + c.
- Here, a = 4, b = -12, and c = 9.
Step 2: Check for Perfect Square
- A perfect square trinomial can be expressed as (my + n)², which expands to m²y² + 2mny + n².
- To check if our expression is a perfect square, we compare:
- m² = 4 (thus, m = 2)
- n² = 9 (thus, n = 3)
Step 3: Verify Middle Term
- The middle term (2m*n) should equal -12y.
- Calculate: 2 * 2 * 3 = 12; since we need -12, we consider it as -2 * 2 * 3.
Step 4: Write the Factorised Form
- Therefore, we can write the expression as:
- 4y² - 12y + 9 = (2y - 3)².
Conclusion
- The correct factorisation of the given quadratic expression is (2y - 3)², which corresponds to option 'D'.
- This confirms that option 'D' is indeed the correct answer, as it demonstrates that the quadratic can be expressed as a square of a binomial.
To factorise the quadratic expression 4y² - 12y + 9, we need to identify the coefficients and apply the factorisation techniques.
Step 1: Identify Coefficients
- The given expression is in the form of ax² + bx + c.
- Here, a = 4, b = -12, and c = 9.
Step 2: Check for Perfect Square
- A perfect square trinomial can be expressed as (my + n)², which expands to m²y² + 2mny + n².
- To check if our expression is a perfect square, we compare:
- m² = 4 (thus, m = 2)
- n² = 9 (thus, n = 3)
Step 3: Verify Middle Term
- The middle term (2m*n) should equal -12y.
- Calculate: 2 * 2 * 3 = 12; since we need -12, we consider it as -2 * 2 * 3.
Step 4: Write the Factorised Form
- Therefore, we can write the expression as:
- 4y² - 12y + 9 = (2y - 3)².
Conclusion
- The correct factorisation of the given quadratic expression is (2y - 3)², which corresponds to option 'D'.
- This confirms that option 'D' is indeed the correct answer, as it demonstrates that the quadratic can be expressed as a square of a binomial.
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