Question

Which binomial is a factor of 8x^2y^3-18y

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

$8x^2y^3-18y$

Apply exponent rule:   $a^{b+c}=a^ba^c$

$8x^2y^3-18y=8yy^2-18y$    ∵ $x^2y^3=yy^2$

                    $=4\cdot \:2yy^2+9\cdot \:2y$

Factor out common term 2y

                    $=2y\left(4x^2y^2-9\right)$

We know that the Binomial is an expression that consists of two terms. Thus,

(4x²y²- 9) represents the binomial factor of $8x^2y^3-18y$

We can further simplify by Factoring 4x²y² - 9:  (2xy + 3) (2xy - 3)

                      $=2y\left(2xy+3\right)\left(2xy-3\right)$

Here:

(2xy + 3) and (2xy -3) are the binomial factors of $8x^2y^3-18y$ as each of them consists of two terms.