Answer :
To solve this problem, we need to expand the expression [tex]\((A-B)^2\)[/tex], where [tex]\(A = n \cdot x\)[/tex] and [tex]\(B = m\)[/tex]. We are given specific values [tex]\(n = 6\)[/tex] and [tex]\(m = 5\)[/tex]. This means:
- [tex]\(A = 6x\)[/tex]
- [tex]\(B = 5\)[/tex]
Now, let's expand the expression [tex]\((A-B)^2\)[/tex]:
[tex]\[
(A-B)^2 = (6x - 5)^2
\][/tex]
Using the formula for the square of a binomial, [tex]\((a-b)^2 = a^2 - 2ab + b^2\)[/tex], we can expand [tex]\((6x - 5)^2\)[/tex]:
1. Calculate [tex]\(a^2\)[/tex]:
[tex]\[
(6x)^2 = 36x^2
\][/tex]
2. Calculate [tex]\(-2ab\)[/tex]:
[tex]\[
-2 \cdot (6x) \cdot 5 = -60x
\][/tex]
3. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
Putting it all together:
[tex]\[
(6x - 5)^2 = 36x^2 - 60x + 25
\][/tex]
Now, compare this expanded expression with the given options:
a) [tex]\(36x^2 + 60x + 25\)[/tex]
b) [tex]\(36x^2 + 60x - 25\)[/tex]
c) [tex]\(36x^2 - 60x + 25\)[/tex]
d) [tex]\(36x^2 - 60x - 25\)[/tex]
The option that matches the expanded expression [tex]\(36x^2 - 60x + 25\)[/tex] is option c). Therefore, the trinomial [tex]\(36x^2 - 60x + 25\)[/tex] is equivalent to [tex]\((A-B)^2\)[/tex].
- [tex]\(A = 6x\)[/tex]
- [tex]\(B = 5\)[/tex]
Now, let's expand the expression [tex]\((A-B)^2\)[/tex]:
[tex]\[
(A-B)^2 = (6x - 5)^2
\][/tex]
Using the formula for the square of a binomial, [tex]\((a-b)^2 = a^2 - 2ab + b^2\)[/tex], we can expand [tex]\((6x - 5)^2\)[/tex]:
1. Calculate [tex]\(a^2\)[/tex]:
[tex]\[
(6x)^2 = 36x^2
\][/tex]
2. Calculate [tex]\(-2ab\)[/tex]:
[tex]\[
-2 \cdot (6x) \cdot 5 = -60x
\][/tex]
3. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
Putting it all together:
[tex]\[
(6x - 5)^2 = 36x^2 - 60x + 25
\][/tex]
Now, compare this expanded expression with the given options:
a) [tex]\(36x^2 + 60x + 25\)[/tex]
b) [tex]\(36x^2 + 60x - 25\)[/tex]
c) [tex]\(36x^2 - 60x + 25\)[/tex]
d) [tex]\(36x^2 - 60x - 25\)[/tex]
The option that matches the expanded expression [tex]\(36x^2 - 60x + 25\)[/tex] is option c). Therefore, the trinomial [tex]\(36x^2 - 60x + 25\)[/tex] is equivalent to [tex]\((A-B)^2\)[/tex].
