Question

РАЗЛОЖИТЕ НА МНОЖИТЕЛИ а) 64а^3-1.....б) 8b^3+а^3....в)8/27а^-1/64b^3.....в)216а^3-b^6

Answer 1

а) 64а^3-1=(4a-1)(16a^2+4a+1)

б) 8b^3+а^3=(2b+a)(4b^2-2ba+a^2)

в)8/27а^3-1/64b^3=(2/3a-1/4b)(4/9a^2+1/6ab+1/16b^2)

в)216а^3-b^6=(6a-b^2)(36a^2+6ab^2+b^4)

Answer 2

Factoring Polynomials

a) 64a^3 - 1

To factor the expression 64a^3 - 1, we can use the difference of cubes formula, which states that a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, we have 64a^3 - 1, which can be expressed as (4a)^3 - 1^3. Applying the difference of cubes formula, we get:

64a^3 - 1 = (4a - 1)(16a^2 + 4a + 1) [[1]]

b) 8b^3 + a^3

The expression 8b^3 + a^3 can be factored using the sum of cubes formula, which states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). In this case, we have 8b^3 + a^3, which can be expressed as (2b)^3 + a^3. Applying the sum of cubes formula, we get:

8b^3 + a^3 = (2b + a)(4b^2 - 2ab + a^2) [[2]]

c) 8/27a^-1/64b^3

To simplify the expression 8/27a^-1/64b^3, we can rewrite it using positive exponents. First, we rewrite a^-1 as 1/a and then simplify the expression:

8/27a^-1/64b^3 = (2/3a)(1/64b^3) = 1/24ab^3 [[3]]

d) 216a^3 - b^6

The expression 216a^3 - b^6 can be factored using the difference of cubes formula. We can express 216a^3 as (6a)^3 and b^6 as (b^2)^3. Applying the difference of cubes formula, we get:

216a^3 - b^6 = (6a - b^2)(36a^2 + 6ab^2 + b^4) [[4]]

These are the factored forms of the given expressions.

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