Question
The binomial y squared minus 49 has y minus 7 as one of its factors. What is the other factor of the binomial?Answer options with 5 options.y.7 y.7 minus yDy minus 7E.y plus 7
Answers
GPT-4o mini
To factor the expression \( y^2 - 49 \), we can recognize that it is a difference of squares. The difference of squares can be factored using the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we have \( a = y \) and \( b = 7 \) because \( 49 = 7^2 \). Therefore, we can write:
\[
y^2 - 49 = (y - 7)(y + 7)
\]
Since \( y - 7 \) is given as one of the factors, the other factor must be \( y + 7 \).
Thus, the other factor of the expression \( y^2 - 49 \) is:
\[
\boxed{y + 7}
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
In this case, we have \( a = y \) and \( b = 7 \) because \( 49 = 7^2 \). Therefore, we can write:
\[
y^2 - 49 = (y - 7)(y + 7)
\]
Since \( y - 7 \) is given as one of the factors, the other factor must be \( y + 7 \).
Thus, the other factor of the expression \( y^2 - 49 \) is:
\[
\boxed{y + 7}
\]