Drag and drop the expressions into the boxes to correctly complete the proof of the polynomial identity.

The proof of the polynomial identity shows that the left side equals the right side. To find what comes next, simplify the left side using order of operations (PEMDAS) by doing the exponent first, combing like terms and then simplifying.

[tex](x^2+y^2)^2[/tex] simplifies to

[tex]x^4 +2x^2y^2+y^4\\\\2x^4+2x^2y^2+2y^4\\2(x^4+x^2y^2+y^4)[/tex]

abidemiokin abidemiokin · Answer 2 · 2020-04-21T03:40:56+02:00

Answer:

- [x⁴+2x²y²+y⁴]

- [2x⁴+2x²y²+2y⁴]

- [2(x⁴+x²y²+y⁴)]

Step-by-step explanation:

Given the polynomial function

(x²+y²)²+x⁴+y⁴ = 2(x⁴+x²y²+y⁴)

Simplifying the left hand side of the equation will provide us with the expression in the box based on each step in the calculation.

To get the expression in the first box, we will expand (x²+y²)² at the left hand side of the equation.

(x²+y²)² = (x²+y²)(x²+y²)

= x⁴+x²y²+x²y²+y⁴

= x⁴+2x²y²+y⁴

The expression in the first box will be [ x⁴+2x²y²+y⁴ ]

The polynomial function will become:

[x⁴+2x²y²+y⁴] + x⁴+y⁴ = 2(x⁴+x²y²+y⁴)

Collecting like terms

x⁴+x⁴+2x²y²+y⁴+y⁴ = 2(x⁴+x²y²+y⁴)

[2x⁴+2x²y²+2y⁴] = 2(x⁴+x²y²+y⁴)

To get the equation in the last box, we will factor out 2 in the left hand side of the polynomial.

[2(x⁴+x²y²+y⁴)] = 2(x⁴+x²y²+y⁴)