Question

Розкладіть на множники: a) 81-a² 6) y² - 4х², B) 64x4 - 100y² г) 1+ x3, д) с3 - 64 .​

Answer 1

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Answer 2

a) 81 - a²:

We can write 81 - a² as a difference of squares: (9)^2 - a^2.

Using the formula for the difference of squares (a² - b²) = (a + b)(a - b), we can factorize it as follows:

81 - a² = (9 + a)(9 - a).

So, the expression 81 - a² can be factored as (9 + a)(9 - a).

b) y² - 4x²:

This expression is a difference of squares: y² - (2x)².

Using the formula for the difference of squares, we can factorize it as follows:

y² - 4x² = (y + 2x)(y - 2x).

So, the expression y² - 4x² can be factored as (y + 2x)(y - 2x).

c) 64x^4 - 100y²:

This expression is a difference of squares: (8x²)² - (10y)².

Using the formula for the difference of squares, we can factorize it as follows:

64x^4 - 100y² = (8x² + 10y)(8x² - 10y).

So, the expression 64x^4 - 100y² can be factored as (8x² + 10y)(8x² - 10y).

d) 1 + x³:

This expression cannot be factored further since it does not have any common factors or a recognizable form for factoring.

e) s³ - 64:

This expression is a difference of cubes: (s)³ - (4)³.

Using the formula for the difference of cubes, we can factorize it as follows:

s³ - 64 = (s - 4)(s² + 4s + 16).

So, the expression s³ - 64 can be factored as (s - 4)(s² + 4s + 16).