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

Sagot :

absor201

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

[tex]8x^2y^3-18y[/tex]

Apply exponent rule:   [tex]a^{b+c}=a^ba^c[/tex]

[tex]8x^2y^3-18y=8yy^2-18y[/tex]    ∵ [tex]x^2y^3=yy^2[/tex]

                    [tex]=4\cdot \:2yy^2+9\cdot \:2y[/tex]

Factor out common term 2y

                    [tex]=2y\left(4x^2y^2-9\right)[/tex]

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

(4x²y²- 9) represents the binomial factor of [tex]8x^2y^3-18y[/tex]

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

                      [tex]=2y\left(2xy+3\right)\left(2xy-3\right)[/tex]

Here:

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

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