Question

1. \\((2x - 7)(5x^2 - 3x - 1)\\)\
2. \\((x + 2)(x - 3)(x + 1)\\)

Explanation:

Step1: Distribute $2x$ to trinomial

$2x \cdot 5x^2 + 2x \cdot (-3x) + 2x \cdot (-1) = 10x^3 - 6x^2 - 2x$

Step2: Distribute $-7$ to trinomial

$-7 \cdot 5x^2 + (-7) \cdot (-3x) + (-7) \cdot (-1) = -35x^2 + 21x + 7$

Step3: Combine like terms

$10x^3 - 6x^2 - 2x - 35x^2 + 21x + 7 = 10x^3 - 41x^2 + 19x + 7$

Step4: Multiply first two binomials

$(x+2)(x-3) = x^2 - 3x + 2x - 6 = x^2 - x - 6$

Step5: Distribute trinomial to $(x+1)$

$(x^2 - x - 6)(x+1) = x^2 \cdot x + x^2 \cdot 1 - x \cdot x - x \cdot 1 -6 \cdot x -6 \cdot 1$

Step6: Simplify and combine like terms

$x^3 + x^2 - x^2 - x -6x -6 = x^3 -7x -6$

Answer:

1. $10x^3 - 41x^2 + 19x + 7$
2. $x^3 -7x -6$