Please help me solve these equations

Question

Prove, algebraically, that the following equations are polynomial identities. Show all of your work and explain each step.



3. 

 

4. 

Answer 1

(2x+5)^2 = 4x^2 +20x + 25 for the left side, using FOIL

the right side = 4x(x+5)+25 = 4x^2 +20x +25 using distributive property

they're equal, equivalent, identical, an identity

plug in any value for x and the left and right sides are the same

(4x+6y)(x-2y) = 4x^2 -2xy-12y^2 (Use FOIL, combine the O and I terms, O is for outside: 4x times -2y = -8xy. I is for Inside terms: 6y times x = 6xy. combine them to get 6xy-8xy = -2xy) for the left side

2(2x^2-xy-6) = 4x^2 -2xy -12 (using distributive property of multiplication, multiply 2 times each of the 3 terms in parentheses) for the right side

the left and right sides are equal, equivalent, and equal regardless what value of x you plug into the equation. It's an identity.