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What is the numerical coefficient of the a^8b^2 term in the expansion of (1/3a^2−3b)^6 ? Enter your answer, in simplest fractional form.

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indrawboy

The numerical coefficient of the a⁸b² : 1.6

Further explanation

The main composition of algebraic expressions are:

  • • 1. phrases / terms

algebraic forms separated by arithmetic operations, can be in the form of numbers, variables or a combination of both

consists of one phrase (monomial) to many phrases (polynomial)

  • • 2. variable

is a value that can be changed, its value is unknown, can be in the form of letters, for example, x, y, a, b, etc.

  • • 3. constants

is a fixed value, can be a number, which stands alone without variables

  • • 4. arithmetic operations

  , -, x ,:

  • • 5. coefficients

is a number or letter in front of the variable

  • • 6. exponent

is a number that shows a repetition in multiplication

Expansion from (a + b)⁶

a⁶ + 6a⁵b + 15a⁴b² + 20a³b³ + 15a²b⁴ + 6ab5 + b⁶

Term that fulfills a⁸b² :  15a⁴b² because :

[tex]\displaystyle a=\frac{1}{3}a^2~and~b=-3b[/tex]

so :

[tex]\displaystyle =15(\frac{1}{3}a^2)^4(-3b)^2\\\\=15(\frac{a^8}{3^4})(9b^2)\\\\=\frac{15\times 9}{3^4}a^8b^2\\\\=1.6a^8b^2[/tex]

Learn more

Algebraic expressions

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Keywords : the numerical coefficient, the expansion

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