Asked by Landon Sharp
Multiply. Express your answer as a polynomial in standard form. (1 point)
(6x−7)(6x+7)=
(
6
𝑥
−
7
)
(
6
𝑥
+
7
)
=
Check Answer
(6x−7)(6x+7)=
(
6
𝑥
−
7
)
(
6
𝑥
+
7
)
=
Check Answer
Answers
Answered by
GPT-4o mini
To multiply the two binomials \((6x - 7)(6x + 7)\), we can use the distributive property (also known as the FOIL method for binomials):
\[
(6x - 7)(6x + 7) = 6x \cdot 6x + 6x \cdot 7 - 7 \cdot 6x - 7 \cdot 7
\]
Calculating each part:
1. \(6x \cdot 6x = 36x^2\)
2. \(6x \cdot 7 = 42x\)
3. \(-7 \cdot 6x = -42x\)
4. \(-7 \cdot 7 = -49\)
Now, combining all these terms together:
\[
36x^2 + 42x - 42x - 49
\]
The \(42x\) and \(-42x\) cancel each other out:
\[
36x^2 - 49
\]
So, the final answer in standard form is:
\[
\boxed{36x^2 - 49}
\]
\[
(6x - 7)(6x + 7) = 6x \cdot 6x + 6x \cdot 7 - 7 \cdot 6x - 7 \cdot 7
\]
Calculating each part:
1. \(6x \cdot 6x = 36x^2\)
2. \(6x \cdot 7 = 42x\)
3. \(-7 \cdot 6x = -42x\)
4. \(-7 \cdot 7 = -49\)
Now, combining all these terms together:
\[
36x^2 + 42x - 42x - 49
\]
The \(42x\) and \(-42x\) cancel each other out:
\[
36x^2 - 49
\]
So, the final answer in standard form is:
\[
\boxed{36x^2 - 49}
\]