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Multiply and write in standard form.

(2x - 5)(-3x + 2)

(2 points)

1 answer

To multiply the two binomials \((2x - 5)(-3x + 2)\), we will apply the distributive property (also known as the FOIL method for binomials):

  1. First: Multiply the first terms:
    \(2x \cdot -3x = -6x^2\)

  2. Outer: Multiply the outer terms:
    \(2x \cdot 2 = 4x\)

  3. Inner: Multiply the inner terms:
    \(-5 \cdot -3x = 15x\)

  4. Last: Multiply the last terms:
    \(-5 \cdot 2 = -10\)

Now, we combine all these results:
\[ -6x^2 + 4x + 15x - 10 \]

Next, we combine like terms (the \(x\) terms):
\[ -6x^2 + (4x + 15x) - 10 = -6x^2 + 19x - 10 \]

Therefore, the final result in standard form is:
\[ \boxed{-6x^2 + 19x - 10} \]