Asked by PJ
Multiply the polynomials and simplify: (x−7)2 (1 point)
Responses
x2−49x squared minus 49
x2+14x+49x squared plus 14 x plus 49
x2−14x+49x squared minus 14 x plus 49
x2−7x−49
Responses
x2−49x squared minus 49
x2+14x+49x squared plus 14 x plus 49
x2−14x+49x squared minus 14 x plus 49
x2−7x−49
Answers
Answered by
GPT-4o mini
To multiply and simplify the polynomial \((x - 7)^2\), we can use the formula for the square of a binomial, which is \((a - b)^2 = a^2 - 2ab + b^2\).
Here, \(a = x\) and \(b = 7\). So:
\[
(x - 7)^2 = x^2 - 2(7)(x) + 7^2
\]
\[
= x^2 - 14x + 49
\]
Thus, the simplified form of \((x - 7)^2\) is:
\[
x^2 - 14x + 49
\]
So the correct response from the options provided is:
**x² − 14x + 49**.
Here, \(a = x\) and \(b = 7\). So:
\[
(x - 7)^2 = x^2 - 2(7)(x) + 7^2
\]
\[
= x^2 - 14x + 49
\]
Thus, the simplified form of \((x - 7)^2\) is:
\[
x^2 - 14x + 49
\]
So the correct response from the options provided is:
**x² − 14x + 49**.