Binomio eta monomio baten biderketa Aldatu Monomio bat eta binomio bat biderkatzen direnean, erregela hau jarraitu behar da:
c
(
a
+
b
)
=
c
a
+
c
b
{\displaystyle c(a+b)=ca+cb\,}
c gaiari faktore komuna deritzo.
a
+
b
×
c
c
a
+
c
b
{\displaystyle {\begin{array}{rrr}&a&+b\\\times &&c\\\hline &ca&+cb\end{array}}}
Adibidez,
3
x
(
4
x
−
6
y
)
=
(
3
x
)
(
4
x
)
+
(
3
x
)
(
−
6
y
)
=
12
x
2
−
18
x
y
{\displaystyle 3x(4x-6y)=(3x)(4x)+(3x)(-6y)=12x^{2}-18xy\,}
Bi binomioen biderketa Aldatu Bi binomio honela biderkatzen dira:
(
a
+
b
)
(
c
+
d
)
=
a
b
+
a
d
+
b
c
+
b
d
{\displaystyle (a+b)(c+d)=ab+ad+bc+bd\,}
Binomio baten karratua Aldatu Binomio baten karratua osatzen:
(a+b)2 =a2 +2ab+b2 .
Binomio baten karratua honela osatzen da:
(
a
+
b
)
2
=
(
a
+
b
)
×
(
a
+
b
)
{\displaystyle (a+b)^{2}=(a+b)\times (a+b)\,}
Garatuz:
a
+
b
×
a
+
b
+
a
b
+
b
2
a
2
+
a
b
a
2
+
2
a
b
+
b
2
{\displaystyle {\begin{array}{rrr}&a&+b\\\times &a&+b\\\hline &+ab&+b^{2}\\a^{2}&+ab&\\\hline a^{2}&+2ab&+b^{2}\end{array}}}
Labur:
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
{\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}\,}
Adibidez:
(
x
+
3
)
2
=
x
2
+
2
×
3
×
x
+
3
2
=
x
2
+
6
x
+
9
{\displaystyle (x+3)^{2}=x^{2}+2\times 3\times x+3^{2}=x^{2}+6x+9\,}
Binomioko gaien kenketa egiten denean berriz:
(
a
−
b
)
2
=
(
a
−
b
)
×
(
a
−
b
)
{\displaystyle (a-b)^{2}=(a-b)\times (a-b)}
Gaiz gai biderkatuz:
a
−
b
×
a
−
b
−
a
b
+
b
2
a
2
−
a
b
a
2
−
2
a
b
+
b
2
{\displaystyle {\begin{array}{rrr}&a&-b\\\times &a&-b\\\hline &-ab&+b^{2}\\a^{2}&-ab&\\\hline a^{2}&-2ab&+b^{2}\end{array}}}
Labur:
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
{\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}\,}
Adibidez,
(
2
x
−
3
y
)
2
=
4
x
2
−
12
x
y
+
9
y
2
{\displaystyle (2x-3y)^{2}=4x^{2}-12xy+9y^{2}\,}
Binomio konjugatuak Aldatu Binomio konjugatuen biderketa:
(a+b)(a-b)=a2 -b2 Binomio konjugatuen biderketa honela definitzen da:
(
a
+
b
)
(
a
−
b
)
{\displaystyle (a+b)(a-b)\,}
Gaiz gai:
a
+
b
×
a
−
b
−
a
b
−
b
2
a
2
+
a
b
a
2
−
b
2
{\displaystyle {\begin{array}{rrr}&a&+b\\\times &a&-b\\\hline &-ab&-b^{2}\\a^{2}&+ab&\\\hline a^{2}&&-b^{2}\end{array}}}
Labur:
(
a
+
b
)
(
a
−
b
)
=
a
2
−
b
2
{\displaystyle (a+b)(a-b)=a^{2}-b^{2}\,}
Adibidez:
(
3
x
+
5
y
)
(
3
x
−
5
y
)
=
(
3
x
)
2
−
(
5
y
)
2
=
9
x
2
−
25
y
2
{\displaystyle (3x+5y)(3x-5y)=(3x)^{2}-(5y)^{2}=9x^{2}-25y^{2}\,}
Datuak: Q193623
Multimedia: Binomial theorem
