2. (a+b)(a-b)=a^2-b^2
3. (x+a)(x+b)=x^2+(a+b)x+ab
4. (ax+b)(cx+d)=acx^2+(ad+dc)x+bd
5. (a±b)^3=a^3±3a^2b+3ab^2±b^3 (複号同順)
6. (a±b)(a^2干ab+b^2)=a^3±b^3 (複号同順)
7. (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca
註：＾はべき乗です
1.
(a+b)^2
=(a+b)(a+b)
=a^2+ab+ba+b^2
=a^2+2ab+b^2
(a-b)^2
=(a-b)(a-b)
=a^2-ab-ba+b^2
=a^2-2ab+b^2
2.
(a+b)(a-b)
=a^2-ab+ba-b^2
=a^2-b^2
3.
(x+a)(x+b)
=x^2+bx+ax+ab
=x^2+(a+b)x+ab
4.
(ax+b)(cx+d)
=acx^2+adx+bcx+bd
=acx^2+(ad+bc)x+bd
5.
(a+b)^3
=(a+b)(a+b)^2
=(a+b)(a^2+2ab+b^2)
=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3
=a^3+3a^2b+3ab^2+b^3
(a-b)^3
=(a-b)(a-b)^2
=(a-b)(a^2-2ab+b^2)
=a^3-2a^2b+ab^2-a^2b+2ab^2-b^3
=a^3-3a^2b+3ab^2-b^3
6.
(a+b)(a^2-ab+b^2)
=a^3-a^2b+ab^2+a^2b-ab^2+b^3
=a^3+b^3
(a-b)(a^2+ab+b^2)
=a^3+a^2b+ab^2-a^2b-ab^2-b^3
=a^3-b^3
7.
(a+b+c)^2
=(a+b+c)(a+b+c)
=a^2+ab+ac+ba+b^2+bc+ca+cb+c^2
=a^2+b^2+c^2+2ab+2bc+2ca
(a+b)^2
=(a+b)(a+b)
=a^2+ab+ba+b^2
=a^2+2ab+b^2
(a-b)^2
=(a-b)(a-b)
=a^2-ab-ba+b^2
=a^2-2ab+b^2
2.
(a+b)(a-b)
=a^2-ab+ba-b^2
=a^2-b^2
3.
(x+a)(x+b)
=x^2+bx+ax+ab
=x^2+(a+b)x+ab
4.
(ax+b)(cx+d)
=acx^2+adx+bcx+bd
=acx^2+(ad+bc)x+bd
5.
(a+b)^3
=(a+b)(a+b)^2
=(a+b)(a^2+2ab+b^2)
=a^3+2a^2b+ab^2+a^2b+2ab^2+b^3
=a^3+3a^2b+3ab^2+b^3
(a-b)^3
=(a-b)(a-b)^2
=(a-b)(a^2-2ab+b^2)
=a^3-2a^2b+ab^2-a^2b+2ab^2-b^3
=a^3-3a^2b+3ab^2-b^3
6.
(a+b)(a^2-ab+b^2)
=a^3-a^2b+ab^2+a^2b-ab^2+b^3
=a^3+b^3
(a-b)(a^2+ab+b^2)
=a^3+a^2b+ab^2-a^2b-ab^2-b^3
=a^3-b^3
7.
(a+b+c)^2
=(a+b+c)(a+b+c)
=a^2+ab+ac+ba+b^2+bc+ca+cb+c^2
=a^2+b^2+c^2+2ab+2bc+2ca
