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Question

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1. Which of the following equations is a polynomial identity?

a. 

b. 

c. 

d. 

2. Which expression is not equivalent to ?

a. 

b. 

c. 

d. 

Prove, algebraically, that the following equations are polynomial identities. Show all of your work and explain each step. Use the Rubric as a reference for what is expected for each problem. 

3. 

 

4. 

 

Answer 1

1) c is the identity

2) d is not equivalent to 16x^4 - y^4. It has 2 extra terms.

3) (2x+5)^2 = (2x+5)(2x+5) = 4x^2 +10x+10x +25 = 4x^2+20x +25

then simplify the right side 4x(x+5) +25 = 4x^2 +20x +25.

both sides are identical

4) for the right side, use FOIL: (4x+6y)(x-2y) = 4x^2-8xy+6xy -12y^2

= 4x^2 -2xy-12y^2

then simplify the right side, use the distributive property: 2(2x^2-xy-6y^2) = 4x^2-2xy-12y^2

both sides are equivalent. It's an identity because any value of (x,y) will satisfy both sides of the equation.