The values are [tex]A=8, B=5, C= 20[/tex] and [tex]D=3[/tex]
Explanation:
The expression is [tex]4x^{2} (2x^{3} +5x)=Ax^{B} +Cx^{D}[/tex]
Simplifying, we get,
[tex]8x^{5} +20x^3=Ax^{B} +Cx^{D}[/tex]
Since, both sides of the expression are equal, we can equate the corresponding values of A, B, C and D.
Thus, we get,
[tex]8 x^{5}=A x^{B}[/tex] ⇒ [tex]A=8[/tex] and [tex]B=5[/tex]
Also, equating, [tex]20 x^{3}=C x^{D}[/tex], we get,
[tex]C=20[/tex] and [tex]D=3[/tex]
Thus, the values are [tex]A=8, B=5, C= 20[/tex] and [tex]D=3[/tex]
