Ta có: (x+a)(x+b)(x+c) = x3 + (a+b+c)x2 +(ab+bc+ca)x + abc

VT = (x2+ax+bx+ab)(x+c)

= x3 + ax2 + bx2 + abx + cx2 + cax + bcx + abc (1)

VP = x3 + (a+b+c)x2 +(ab+bc+ca)x + abc

= x3 + ax2 + bx2 + abx + cx2 + cax + bcx + abc (2)

Từ (1) và (2), suy ra:

(x+a)(x+b)(x+c) = x3 + (a+b+c)x2 +(ab+bc+ca)x + abc

Bài 1 CMR

1. ( a+b) 2= a2 + 2ab+ b2

2. ( a-b) 2 = a2 -2ab + b2

3.( a-b) ( a+b)=a2 -b2

4.( a+b)3 = a3 + 3a2b+3ab2 + b3

5. ( a-b) 3 =a3 - 3a2b + 3ab2

1) (a+b)^2

=(a+b)(a+b)

=a^2+ab+ab+b^2

=a^2+2a+b^2

2) (a-b)^2

=(a-b)(a-b)

=a^2-ab-ab+b^2

=a^2-2ab+b^2

3)(a-b)(a+b)

=a^2+ab-ab-b^2

=a^2-b^2

4) (a+b)^3

=(a+b)^2(a+b)

=(a^2+2ab+b^2)(a+b) ( chứng minh câu a)

=a^3+a^2b+2ab^2+2a^2b+ab^2+b^3

=a^3+3a^2b+3ab^2+b^3

5) (a-b)^3

=(a-b)^2(a-b)

=(a^2-2ab+b^2)(a-b) ( chứng minh câu b)

=a^3-a^2b+2ab^2-2a^2b+ab^2-b^3

=a^3-3a^2b+3ab^2-b^3