Find expert advice and community support for all your questions on IDNLearn.com. Discover detailed answers to your questions with our extensive database of expert knowledge.

Factor [tex]$4b^2 - 9$[/tex].

A. [tex]$(2b + 3)(2b - 3)$[/tex]

B. [tex][tex]$(4b + 3)(b - 3)$[/tex][/tex]

C. [tex]$(2b - 4)(2b - 5)$[/tex]


Sagot :

To factor the quadratic expression [tex]\(4b^2 - 9\)[/tex], you can use the difference of squares method.

Here's the step-by-step solution:

1. Identify the pattern:
The expression [tex]\(4b^2 - 9\)[/tex] is in the form of [tex]\(a^2 - c^2\)[/tex], which is a difference of squares. The difference of squares can be factored using the formula:
[tex]\[ a^2 - c^2 = (a - c)(a + c) \][/tex]

2. Rewrite the terms:
Notice that [tex]\(4b^2\)[/tex] is a perfect square and so is [tex]\(9\)[/tex]. Specifically:
[tex]\[ 4b^2 = (2b)^2 \quad \text{and} \quad 9 = 3^2 \][/tex]
So, we can rewrite the expression [tex]\(4b^2 - 9\)[/tex] as:
[tex]\[ (2b)^2 - 3^2 \][/tex]

3. Apply the difference of squares formula:
Using the formula [tex]\(a^2 - c^2 = (a - c)(a + c)\)[/tex], we get:
[tex]\[ (2b - 3)(2b + 3) \][/tex]

Therefore, the factored form of [tex]\(4b^2 - 9\)[/tex] is:
[tex]\[ (2b - 3)(2b + 3) \][/tex]

The given answer options include [tex]\((2b + 3)(2b - 3)\)[/tex], which is equivalent to our result [tex]\( (2b - 3)(2b + 3) \)[/tex] due to the commutative property of multiplication.

Hence, the correct factored form of the expression [tex]\(4b^2 - 9\)[/tex] is:
[tex]\[ (2b - 3)(2b + 3) \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.