Question

Answer 1

1. \(\left(3+xy^2\right)^2=9+6xy^2+x^2y^4\)

2. \(\left(10-2m^2n\right)^2=100-40m^2n+4m^4n^2\)

3. \(\left(a-b^2\right)\left(a+b^2\right)=a^2-b^4\)

4. \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)=\left(a^2+2a\right)^2-3^2=a^4+4a^3+4a^2-9\)

5. \(\left(2y-1\right)^3=8y^3-12y^2+6y-1\)

6. \(\left(2y-5\right)\left(4y^2+10y+25\right)=8y^3-125\)

Answer 2

1: \(\left(xy^2+3\right)^2=x^2y^4+6xy^2+9\)

2: \(\left(10-2m^2n\right)^2=100-40m^2n+4m^4n^2\)

3: \(\left(a-b^2\right)\left(a+b^2\right)=a^2-b^4\)

4: \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)

\(=\left(a^2+2a\right)^2-9\)

\(=a^4+4a^3+4a^2-9\)

5: \(\left(2y-1\right)^3=8y^3-12y^2+6y-1\)

6: \(\left(2y-5\right)\left(4y^2+10y+25\right)=8y^3-125\)