Question

\(a,\left(a+b\right)^2-\left(a-b\right)^2\)

\(b,\left(a+b\right)^3-\left(a-b\right)^3-2b^3\)

Answer 1

\(a,\left(a+b\right)^2-\left(a-b\right)^2\)

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

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

\(=4ab\)

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

\(=\left(a^3+3a^2b+3ab^2+b_{ }^3\right)-\left(a^3-3a^2b+3ab^2-b^3\right)-2b^3\)

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

\(=6a^2b\)

Answer 2

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

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

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

\(=4ab\)

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

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

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

\(=6a^2b+2b^3-2b^3\)

\(=6a^2b\)

Answer 3

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

Answer 4

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

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

=4ab

b, (a + b)^3 - (a - b)^3 - 2b^3

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

=6a^2b