headleym7
Answered

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Factor:

81y² - 100

Select the correct answer below:

A. (9y - 10)(9y - 10)
B. (9y + 10)(9y + 10)
C. (9y - 10)
D. (9y + 10)(9y - 10)

Sagot :

GinnyAnswer
To factor the given expression [tex]\( 81 y^2 - 100 \)[/tex], follow these steps:

1. Express in Standard Form:
The given expression is [tex]\( 81 y^2 - 100 \)[/tex].

2. Identify as a Difference of Squares:
Notice that [tex]\( 81 y^2 - 100 \)[/tex] is a difference of squares. Recall the formula for factoring a difference of squares:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]

3. Rewrite Each Term as a Square:
Recognize that [tex]\( 81 y^2 = (9y)^2 \)[/tex] and [tex]\( 100 = 10^2 \)[/tex]. Thus, the expression can be rewritten as:
[tex]\[ (9 y)^2 - 10^2 \][/tex]

4. Apply the Difference of Squares Formula:
Using the difference of squares formula:
[tex]\[ (9 y)^2 - 10^2 = (9 y - 10)(9 y + 10) \][/tex]

5. Confirm the Factors:
The expression [tex]\( 81 y^2 - 100 \)[/tex] factors to [tex]\((9 y - 10)(9 y + 10)\)[/tex].

Therefore, the correct factorization is obtained, and the correct answer among the given choices is:
[tex]\[ (9 y + 10)(9 y - 10) \][/tex]
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