Question

Prove the polynomial identity.
x^2-y^2=(x-y)(x+y)

Answer 1

"difference of squares" formula

can be proved going backwards

multiply the answer on the right side of the equal to see if you get the left side of the equal sign

by using the distributive property of multiplication over addition to expand the right-hand side of the equation, as follows:

(a + b)(a - b) = a(a - b) + b(a - b) = a^2 - ab + ab - b^2 = a^2 - b^2

let x = 8

let y = 5

8^2-5^2=(8-5)(8+5)

64-25 = 39

(8-5)(8+5) = (3)(13) = 39

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