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Mathematics
Problem
Which algebraic identity is most suitable to simplify the numerator in the expression
lim
x
→
5
x
2
−
25
x
−
5
\lim_{x\to 5}\dfrac{x^{2}-25}{x-5}
lim
x
→
5
x
−
5
x
2
−
25
so that the limit can be evaluated? a)
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
(a-b)^{2}=a^{2}-2ab+b^{2}
(
a
−
b
)
2
=
a
2
−
2
ab
+
b
2
b)
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
ab
+
b
2
)
c)
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
a^{2}-b^{2}=(a-b)(a+b)
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
d)
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
(a+b)^{2}=a^{2}+2ab+b^{2}
(
a
+
b
)
2
=
a
2
+
2
ab
+
b
2
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