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

All the given expressions are binomials except the expression in (i) which is a trinomial.

What are binomials in expressions?

Binomials can be defined as the expression that contains two variables that are different in terms.

ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴

= 10x⁵-10x⁴+3x⁵-6x⁵

= 7x⁵+10x⁴ (this is an example of a binominal)

iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)

iv.) 5(a-1)-10(a-1)+100(a-1)

= 5a-5-10a+10+100a-100

= 95a - 95 (binomials)

v.) (2πr-πr²)r-(2πr-πr²)2r

= 2πr²-πr³-4πr²+2πr³

= -2πr²+πr³(binomials)

Answer 2

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