Multiplying Function
f(x) 9(x)
1.(4x2 (3x+2)
2.(x+10) (7x-6)
3.(2x+9) (3x-6)
4.(3x²-2) (x+2)
5.(8x+15) (2x²-2)

Let's multiply each pair of functions step by step:### 1. \( (4x^2) \cdot (3x + 2) \)Distribute \( 4x^2 \) over \( 3x + 2 \):\[4x^2 \cdot (3x + 2) = 4x^2 \cdot 3x + 4x^2 \cdot 2\]\[= 12x^3 + 8x^2\]### 2. \( (x + 10) \cdot (7x - 6) \)Distribute \( x + 10 \) over \( 7x - 6 \):\[(x + 10) \cdot (7x - 6) = x \cdot 7x + x \cdot (-6) + 10 \cdot 7x + 10 \cdot (-6)\]\[= 7x^2 - 6x + 70x - 60\]\[= 7x^2 + 64x - 60\]### 3. \( (2x + 9) \cdot (3x - 6) \)Distribute \( 2x + 9 \) over \( 3x - 6 \):\[(2x + 9) \cdot (3x - 6) = 2x \cdot 3x + 2x \cdot (-6) + 9 \cdot 3x + 9 \cdot (-6)\]\[= 6x^2 - 12x + 27x - 54\]\[= 6x^2 + 15x - 54\]### 4. \( (3x^2 - 2) \cdot (x + 2) \)Distribute \( 3x^2 - 2 \) over \( x + 2 \):\[(3x^2 - 2) \cdot (x + 2) = 3x^2 \cdot x + 3x^2 \cdot 2 - 2 \cdot x - 2 \cdot 2\]\[= 3x^3 + 6x^2 - 2x - 4\]### 5. \( (8x + 15) \cdot (2x^2 - 2) \)Distribute \( 8x + 15 \) over \( 2x^2 - 2 \):\[(8x + 15) \cdot (2x^2 - 2) = 8x \cdot 2x^2 + 8x \cdot (-2) + 15 \cdot 2x^2 + 15 \cdot (-2)\]\[= 16x^3 - 16x + 30x^2 - 30\]\[= 16x^3 + 30x^2 - 16x - 30\]These are the simplified forms of the products for each function pair.

Answered by characterailangako | 2024-09-02