Binomio

c(a+b)=ca+cb. c faktore komuna da.

Monomio bat eta binomio bat biderkatzen direnean, erregela hau jarraitu behar da:

${\displaystyle c(a+b)=ca+cb\,}$

c gaiari faktore komuna deritzo.

${\displaystyle {\begin{array}{rrr}&a&+b\\\times &&c\\\hline &ca&+cb\end{array}}}$

Adibidez,

${\displaystyle 3x(4x-6y)=(3x)(4x)+(3x)(-6y)=12x^{2}-18xy\,}$

Bi binomio honela biderkatzen dira:

${\displaystyle (a+b)(c+d)=ab+ad+bc+bd\,}$

Binomio baten karratua osatzen: (a+b)²=a²+2ab+b².

Binomio baten karratua honela osatzen da:

${\displaystyle (a+b)^{2}=(a+b)\times (a+b)\,}$

Garatuz:

${\displaystyle {\begin{array}{rrr}&a&+b\\\times &a&+b\\\hline &+ab&+b^{2}\\a^{2}&+ab&\\\hline a^{2}&+2ab&+b^{2}\end{array}}}$

Labur:

${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}\,}$

Adibidez:

${\displaystyle (x+3)^{2}=x^{2}+2\times 3\times x+3^{2}=x^{2}+6x+9\,}$

Binomioko gaien kenketa egiten denean berriz:

${\displaystyle (a-b)^{2}=(a-b)\times (a-b)}$

Gaiz gai biderkatuz:

${\displaystyle {\begin{array}{rrr}&a&-b\\\times &a&-b\\\hline &-ab&+b^{2}\\a^{2}&-ab&\\\hline a^{2}&-2ab&+b^{2}\end{array}}}$

Labur:

${\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}\,}$

Adibidez,

${\displaystyle (2x-3y)^{2}=4x^{2}-12xy+9y^{2}\,}$

Binomio konjugatuen biderketa: (a+b)(a-b)=a²-b²

Binomio konjugatuen biderketa honela definitzen da:

${\displaystyle (a+b)(a-b)\,}$

Gaiz gai:

${\displaystyle {\begin{array}{rrr}&a&+b\\\times &a&-b\\\hline &-ab&-b^{2}\\a^{2}&+ab&\\\hline a^{2}&&-b^{2}\end{array}}}$

Labur: ${\displaystyle (a+b)(a-b)=a^{2}-b^{2}\,}$

Adibidez:

${\displaystyle (3x+5y)(3x-5y)=(3x)^{2}-(5y)^{2}=9x^{2}-25y^{2}\,}$