Question

11 1) (5x+1)^3 2) (4m+ n) ² 3)p³ + 8q^3

Answer 1

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Answer 2

Sure! Here are the expanded forms of the given expressions:

1. (5x+1)^3: To expand (5x+1)^3, we can use the binomial expansion or the formula for expanding a cube of a binomial:

(5x+1)^3 = (5x)^3 + 3(5x)^2(1) + 3(5x)(1)^2 + (1)^3 = 125x^3 + 3(25x^2)(1) + 3(5x)(1) + 1 = 125x^3 + 75x^2 + 15x + 1

Therefore, the expanded form of (5x+1)^3 is 125x^3 + 75x^2 + 15x + 1.

2. (4m+n)^2: To expand (4m+n)^2, we can use the formula for expanding the square of a binomial:

(4m+n)^2 = (4m)^2 + 2(4m)(n) + (n)^2 = 16m^2 + 8mn + n^2

Therefore, the expanded form of (4m+n)^2 is 16m^2 + 8mn + n^2.

3. p^3 + 8q^3: The expression p^3 + 8q^3 cannot be further expanded since it represents the sum of two cubes, which does not have a simplified form.