Question

PLEASE MATH EXPERT!
I am struggling thank you

Answer 1

`x^(4) -y^(4) +6x^(2)y+9y^(2)`

Explanation:

This is just a big multiplication, but it gets more simple when you break it into steps.

First consider
`x^(2) (x^(2) +3y-y^(2) )`. This multiplies out to
`x^(4) +3x^(2)y-x^(2)y^(2)`

Next,
`3y(x^(2) +3y-y^(2) )`. This is
`3x^(2)y+9y^(2)-3y^(3)`

Finally,
`y^(2) (x^(2)+3y-y^(2))`. This is
`x^(2)y^(2) +3x^(3)-y^(4)`

Sum these three expressions together and you get
`x^(4) -y^(4) +6x^(2)y+9y^(2)`

Answer 2

Explanation:

(x² + 3y + y²)(x² + 3y - y²)

= x²*(x² + 3y - y²) + 3y*(x² + 3y - y²) + y²((x² + 3y - y²)

= ( x²*x² + x²*3y - x²*y²) + [3y*x² + 3y*3y - 3y*y²] + {y²*x² + y²*3y - y²*y²}

= x⁴ + 3x²y - x²y² + 3x²y + 9y² - 3y³ + x²y² + 3y³ - y⁴

= x⁴ + 3x²y + 3x²y - x²y² + x²y² + 9y² - 3y³ + 3y³ - y⁴

= x⁴ + 6x²y + 0 + 9y² + 0 - y⁴

= x⁴ + 6x²y + 9y² - y⁴

Hint:

`x^(2) *x^(2) = x^(2+2)=x^(4)\\\\3y * 3y = 3*3 * y^(1+1) = 9y^(2)\\\\`