Question

Celina says that each of the following expressions is actually a binomial in disguise:(Expressions in picture) For example, she sees that the expression in (i) it is algebraically equivalent to − , which is indeed a binomial. (She is happy to write this as + (−), if you prefer.) Is she right about the remaining four expressions?

Answer 1

Yes , she is right. All the remaining can be expressed in binomial.

II) $5x^3 * 2x^2 - 10x^4 + 3x^5 + 3x * (-2)x^4$

$10x^5 - 10x^4 + 3x^5 + -6x^5= 7x^5 - 10x^4$ is a binomial

iii) $(t+2)^2 - 4t = t^2 + 4t + 4 -4t = t^2 + 4$ is a binomial

iv) $5(a-1) - 10(a-1) + 100 ( a-1) = 5a - 5 - 10a + 10 + 100a -100 = 95a -95$ is a binomial

v) $( 2\pi r -\pi r^2)r - ( 2\pi r -\pi r^2)2r = 2\pi r^2 -\pi r^3 - 4\pi r^2 + 2\pi r^3$ = $-2\pi r^2 + \pi r^3$ is also a binomial