Question

In the expansion of (2a + 4b) ^ 8 , which of the following are possible variable terms? Explain your reasoning. a ^ 2 * b ^ 3; a ^ 8 * a ^ 5 * b ^ 3; a * b ^ 8; a ^ 3 * b ^ 5 * a ^ 7 * b * a ^ 6 * b ^ 5; b ^ 8

Answer 1

In the expansion of (2a + 4b)⁸ , the possible variable terms are a⁸ , a⁵b³ , a³b⁵ , a⁷b and b⁸

What is a Variable ?

A variable is an alphabet x, y ,z etc denotes the unknown parameters  in an expression .

The expression given is

(2a + 4b)⁸

The given terms that can be part of this expansion is

a²b³ , a⁸ , a⁵b³ , a³b⁵ , a⁷b , ab⁸ and b⁸

(2a + 4b)⁸ = ((2a + 4b)²)⁴

(2a + 4b)⁸ =(2a + 4b)²(2a + 4b)²(2a + 4b)²(2a + 4b)²

(2a + 4b)⁸ = (4a² +16b² +16ab) (4a² +16b² +16ab) (4a² +16b² +16ab) (4a² +16b² +16ab)

On further simplification

(2a + 4b)⁸ = 256a⁸ +4096 a⁷b + 28672a⁶b² +114688a⁵b³ +286720a⁴b⁴+458752a³b⁵+ 458752a²b⁶ +262144ab⁷ +65536b⁸

Therefore in the expansion of (2a + 4b)⁸ , the possible variable terms are a⁸ , a⁵b³ , a³b⁵ , a⁷b and b⁸.

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