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 (given)
= 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 - 3a²
= (-1 - 3)a²
= -4a²

Cancel +3ab and -3ab.

Add and Subtract Polynomials

So
-4a² + 5a + 6
is the answer.