Question
7) And the product. Simplify y \( (2 w-3)(2 w+3) \)
Ask by Gough Johnson. in the United States
Jan 02,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( y = 4w^2 - 9 \)
Solution
To simplify the expression \( y = (2w - 3)(2w + 3) \), you can use the **difference of squares** formula. The difference of squares states that:
\[
(a - b)(a + b) = a^2 - b^2
\]
Applying this formula to your expression:
\[
(2w - 3)(2w + 3) = (2w)^2 - (3)^2 = 4w^2 - 9
\]
So, the simplified form of the product is:
\[
y = 4w^2 - 9
\]
**Final Answer:**
After simplifying, y = 4 w² – 9
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Simplify this solution Mind Expander
To simplify \( y = (2w-3)(2w+3) \), you can recognize that this expression is in the form of a difference of squares, which states \( a^2 - b^2 = (a-b)(a+b) \). Here, \( a = 2w \) and \( b = 3 \). Now, simply applying the formula, we have: \[ y = (2w)^2 - (3)^2 = 4w^2 - 9. \] So, the simplified form is \( y = 4w^2 - 9 \). Now you've got a clean expression to work with! Additionally, remember that the difference of squares is an incredibly handy tool when simplifying polynomials. It can save you a lot of time in factoring and solving quadratic equations! Also, don't forget to distribute properly when working with binomials—it’s a common snare for many learners!
