Question

Expand and simplify (x+3)(x-3)(3x+2)

Answer 1

Answer:

3x³ + 2x² - 27x - 18.

Explanation:

To expand (x+3)(x-3)(3x+2), we can use the distributive property and multiply each term in the first expression by each term in the second expression, and then multiply the result by each term in the third expression.

(x+3)(x-3)(3x+2)

= (x²-3x+3x-9)(3x+2) // Using (a+b)(a-b)
= a² - b²
= (x²-9)(3x+2)
= 3x(x²) + 2x² - 9(3x) - 9(2) // Using distributive property
= 3x³ + 2x² - 27x - 18 // Simplifying

Therefore, (x+3)(x-3)(3x+2) expands and simplifies to 3x³ + 2x² - 27x - 18.

Answer 2

Answer: To expand the expression, we can use the distributive property of multiplication:

(x+3)(x-3)(3x+2)

= (x^2 - 9)(3x+2) // using (a+b)(a-b) = a^2 - b^2

= 3x(x^2) + 2(x^2) - 9(3x) - 18 // using FOIL

= 3x^3 + 2x^2 - 27x - 18

This is the expanded form of the expression.

To simplify further, we can factor out the greatest common factor of the terms:

= 3(x^3 - 9x) + 2(x^2 - 9)

= 3x(x^2 - 9) + 2(x^2 - 9)

= (3x+2)(x^2 - 9)

= (3x+2)(x-3)(x+3)

So, the simplified expression is (3x+2)(x-3)(x+3).