Question

Fiona wrote out the description of each step for her multiplication of the binomial and trinomial (2x – 3)(5x2 – 2x + 7)

Answer 1

See below:

Step-by-step explanation:

2x times 5x^2 = 10x^3

2x times -2x = -4x^2

2x times 7 = 14x

-3 times 5x^2 = -15x^2

-3 times -2x = 6x

-3 times 7 = -21

Answer 2

Fiona expanded the product of the binomial
`\((2x - 3)\)` and the trinomial
`\((5x^2 - 2x + 7)\)` using the FOIL method (First, Outer, Inner, Last). The result of this multiplication is the polynomial
`\(10x^3 - 19x^2 + 20x - 21\).`

Step-by-step explanation:

Fiona followed the FOIL method to multiply each term of the binomial
`\((2x - 3)\)` by each term of the trinomial
`\((5x^2 - 2x + 7)\)`. Here's the step-by-step calculation:

1. First: Multiply the first terms of each binomial:

`\[ (2x) \cdot (5x^2) = 10x^3 \]`

2. Outer: Multiply the outer terms:

`\[ (2x) \cdot (-2x) = -4x^2 \]`

3. Inner: Multiply the inner terms:

`\[ (-3) \cdot (5x^2) = -15x^2 \]`

4. Last: Multiply the last terms of each binomial:

`\[ (-3) \cdot (-2x) = 6x \]`

Now, combine all the terms:

`\[ 10x^3 - 4x^2 - 15x^2 + 6x - 21 \]`

Combine like terms:

`\[ 10x^3 - 19x^2 + 20x - 21 \]`

So, the expanded form of
`\((2x - 3)(5x^2 - 2x + 7)\) is \(10x^3 - 19x^2 + 20x - 21\).`