Question

Розкрий дужки. a) (a³x + ax2)³б) (b²y + by²)³​

Answer 1

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Answer 2

a) To expand the expression (a³x + ax²)³, we can use the binomial expansion formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Applying this formula to our expression, where a = a³x and b = ax², we get:

(a³x + ax²)³ = (a³x)³ + 3(a³x)²(ax²) + 3(a³x)(ax²)² + (ax²)³

Simplifying further, we have:

(a³x + ax²)³ = a^9x^3 + 3a^5x^3 + 3a^5x^3 + a^3x^3 = a^9x^3 + 6a^5x^3 + a^3x^3

Therefore, the expanded form of (a³x + ax²)³ is a^9x^3 + 6a^5x^3 + a^3x^3.

b) Similarly, for the expression (b²y + by²)³, we can apply the binomial expansion formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

In this case, a = b²y and b = by². Substituting these values, we get:

(b²y + by²)³ = (b²y)³ + 3(b²y)²(by²) + 3(b²y)(by²)² + (by²)³

Simplifying further, we have:

(b²y + by²)³ = b^6y^3 + 3b^4y^3 + 3b^4y^3 + b^2y^3 = b^6y^3 + 6b^4y^3 + b^2y^3

Therefore, the expanded form of (b²y + by²)³ is b^6y^3 + 6b^4y^3 + b^2y^3.