Question

PLEASE MATH EXPERT! I am struggling thank you

Answer 1

Answer:

Step-by-step 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:

$x^{2} *x^{2} = x^{2+2}=x^{4}\\\\3y * 3y = 3*3 * y^{1+1} = 9y^{2}$

Answer 2

Answer:

$x^{4} -y^{4} +6x^{2}y+9y^{2}$

Step-by-step 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 $x^{4} -y^{4} +6x^{2}y+9y^{2}$