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Multiply the following binomials:

[tex]\[ (3x - 5)(-x + 4) \][/tex]

Applying the distributive property, the expression becomes:

[tex]\[ (3x)(-x) + (3x)(4) + (-5)(-x) + (-5)(4) \][/tex]

What is the simplified product in standard form?

[tex]\[ \square x^2 + \square x + \square \][/tex]

Sagot :

GinnyAnsweridn
To multiply the binomials [tex]\((3x - 5)(-x + 4)\)[/tex] and simplify the product into standard form, we'll follow the distributive property (also known as the FOIL method for binomials, which stands for First, Outer, Inner, Last).

Here's the step-by-step process:

1. First: Multiply the first terms in each binomial.
[tex]\[ (3x) \cdot (-x) = -3x^2 \][/tex]

2. Outer: Multiply the outer terms.
[tex]\[ (3x) \cdot 4 = 12x \][/tex]

3. Inner: Multiply the inner terms.
[tex]\[ (-5) \cdot (-x) = 5x \][/tex]

4. Last: Multiply the last terms in each binomial.
[tex]\[ (-5) \cdot 4 = -20 \][/tex]

Next, we combine all these products together:
[tex]\[ -3x^2 + 12x + 5x - 20 \][/tex]

Now, combine like terms:
[tex]\[ -3x^2 + (12x + 5x) - 20 = -3x^2 + 17x - 20 \][/tex]

So, the simplified product in standard form is:
[tex]\[ -3x^2 + 17x - 20 \][/tex]

Thus, the expression can be written as:
[tex]\[ -3x^2 + 17x - 20 \][/tex]
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