Question

36+24x+4x²=? 8a³-8b³=? 9ax³+9ay³=?

Answer 1

36+24х+4х²=4(9+6x+x²)=4(3+x)²

8a³-8b³=8(a³-b³)=8(a-b)(a²+ab+b²)

9ax³+9ay³=9a(x³+y³)=9a(x+y)(x²-xy+y²)

Answer 2

Let's solve each of these expressions one by one:

1. 36 + 24x + 4x²: This is a quadratic expression, which can be factored as follows: 4x² + 24x + 36 = 4(x² + 6x + 9) Now, we can further factor the quadratic expression: 4(x + 3)(x + 3) = 4(x + 3)²

2. 8a³ - 8b³: This is the difference of cubes. You can use the formula for the difference of cubes, which is a³ - b³ = (a - b)(a² + ab + b²): 8a³ - 8b³ = 8(a³ - b³) = 8(a - b)(a² + ab + b²)

3. 9ax³ + 9ay³: You can factor out the common factor of 9a from both terms: 9a(x³ + y³)

So, the simplified expressions are:

1. 36 + 24x + 4x² = 4(x + 3)²
2. 8a³ - 8b³ = 8(a - b)(a² + ab + b²)
3. 9ax³ + 9ay³ = 9a(x³ + y³)