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How do you simplify \[\left( {2x + 3} \right)\left( {2x - 3} \right)?\]

seo-qna
Last updated date: 13th Jun 2024
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Views today: 6.72k
Answer
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372.9k+ views
Hint:This question involves the operation of addition/ subtraction/ multiplication/ division. We need to know the FOIL method to solve these types of questions or we need to know the algebraic formulae to solve this question.

Complete step by step solution:
The given equation is shown below,
\[\left( {2x + 3} \right)\left( {2x - 3} \right) = ?\]
To solve this question we use the FOIL method. Here F means First, O means Outside, I means Inside, L means Last. In the given question we have two binomials in the multiplication process. Let’s solve this,
Firsts: \[2x \times 2x = 4{x^2}\]
Outsides: \[2x \times - 3 = - 6x\]
Inside: \[3 \times 2x = 6x\]
Lasts: \[3 \times - 3 = - 9\]
So, we get
\[\left( {2x + 3} \right)\left( {2x - 3} \right) = \left( {2x \times 2x} \right) + \left( {2x \times - 3}
\right) + \left( {3 \times 2x} \right) + \left( {3 \times - 3} \right)\]
\[
\left( {2x + 3} \right)\left( {2x - 3} \right) = 4{x^2} - 6x + 6x - 9 \\
\left( {2x + 3} \right)\left( {2x - 3} \right) = 4{x^2} - 9 \\
\]
So, the final answer is,
\[\left( {2x + 3} \right)\left( {2x - 3} \right) = 4{x^2} - 9\]


Note:This question involves the operation of addition/ subtraction/ multiplication/ division. Note that the above-mentioned problem can also be solved by using algebraic formula\[\left( {a - b} \right)\left( {a + b} \right) = \left( {{a^2} - {b^2}} \right)\]. So, we take\[\left( {a - b} \right)\]as\[\left( {2x - 3} \right)\]and \[\left( {a + b} \right)\]as\[\left( {2x + 3} \right)\]. So, we get the final answer is\[\left( {{a^2} - {b^2}} \right)\]as\[\left( {4{x^2} - 9} \right)\]. By using this method we can easily find the solution within three steps. We can use either the FOIL method or using the algebraic formula method to solve these types of questions. When multiplying different
sign numbers we would remember the following things,
1) When a negative number is multiplied with the negative number the answer becomes a
positive number.
2) When a negative number is multiplied with the positive number the answer becomes a
negative number.
3) When a positive number is multiplied with the positive number the final answer becomes a positive number.