Multiply a Monomial and a Polynomial

Multiply x and each term of (3x² - 5x + 8).

First multiply x and 3x²: x⋅3x².

Multiply x and -5x: + x⋅(-5x).

Multiply x and +8: + x⋅8.

So x(3x² - 5x + 8) = x⋅3x² + x⋅(-5x) + x⋅8.

x⋅3x² = 3x³
+x⋅(-5x) = -5x²
+x⋅8 = +8x

Product of Powers

So 3x³ - 5x² + 8x is the answer.

Multiply each term of (5 - a + 3b) and a.

First multiply 5 and a: 5⋅a.

Multiply -a and a: -a⋅a.

Multiply +3b and a: +3b⋅a.

Next, multiply -3 (not 3) and each term of (a² + ab - 2).

Multiply -3 and a²: -3⋅a².

Multiply -3 and +ab: -3⋅ab.

Multiply -3 and -2: -3⋅(-2).

So the given expression is
5⋅a - a⋅a + 3b⋅a - 3⋅a² - 3⋅ab - 3⋅(-2).

5⋅a = 5a
- a⋅a = -a²
+3b⋅a = +3ab

-3⋅a² = -3a²
-3⋅ab = -3ab
-3⋅(-2) = +6

-a² and -3a² are like terms.
So -a² - 3a² = (-1 - 3)a² = -4a².

Cancel +3ab and -3ab.
You can cancel these two terms because
+3ab - 3ab = (3 - 3)ab = 0⋅ab = 0.

Add and Subtract Polynomials

So -4a² + 5a + 6 is the answer.