Answer:
[tex]\dfrac{4}{9}x^{5}y-\dfrac{4}{3}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{4}{9}x^2yx(x^2-3xy+y^2)[/tex]
Distribute:
[tex]\implies \dfrac{4}{9}x^2yxx^2-\dfrac{4}{9}x^2yx3xy+\dfrac{4}{9}x^2yxy^2[/tex]
Re-order each term to collect like variables:
[tex]\implies \dfrac{4}{9}x^2x^2xy-\dfrac{4 \cdot 3}{9}x^2xxyy+\dfrac{4}{9}x^2xy^2y[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
(Remembering that a = a¹)
[tex]\implies \dfrac{4}{9}x^{2+2+1}y-\dfrac{12}{9}x^{2+1+1}y^{1+1}+\dfrac{4}{9}x^{2+1}y^{2+1}[/tex]
[tex]\implies \dfrac{4}{9}x^{5}y-\dfrac{12}{9}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}[/tex]
Reduce 12/9 to 4/3:
[tex]\implies \dfrac{4}{9}x^{5}y-\dfrac{4}{3}x^{4}y^{2}+\dfrac{4}{9}x^{3}y^{3}[/tex]
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