Question

A) Cm:a^3-b^3= (a-b)(a^2+ab+b^2)

B) Cm: a^3+b^3=(a+b)(a^2-ab+b^2)

C) Cm: a^2-b^2=(a-b)(a+b)

Answer 1

\(a^3-b^3=\left(a-b\right).\left(a^2+ab+b^2\right)\)

\(\Leftrightarrow\)\(a^3-b^3=a^3+a^2b+ab^2-a^2b-ab^2-b^3\)

\(\Leftrightarrow\)\(a^3-b^3=a^3-b^3\)

\(\Rightarrow\)\(đpcm\)

Answer 2

\(a^3+b^3=\left(a+b\right).\left(a^2-ab+b^2\right)\)

\(\Leftrightarrow\)\(a^3+b^3=a^3-a^2b+ab^2+a^2b-ab^2+b^3\)

\(\Leftrightarrow\)\(a^3+b^3=a^3+b^3\)

\(\Rightarrow\)\(đpcm\)

Answer 3

\(a^2-b^2=\left(a-b\right).\left(a+b\right)\)

\(\Leftrightarrow\)\(a^2-b^2=a^2+ab-ab-b^2\)

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

\(\Rightarrow\)\(đpcm\)

Answer 4

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

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

<=>a^2-b^2=a^2-b^2

=>đpcm