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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.