QuestionMultiply. $(5 c-8)(-4 c+5)$

Studdy Solution

STEP 1

What is this asking? We need to multiply two expressions: $(5c - 8)$ and $(-4c + 5)$ . Watch out! Don't forget to handle the negative signs carefully, and remember to combine like terms correctly!

STEP 2

1. Expand the expression
2. Simplify the expression

STEP 3

Let's distribute the first term of the first expression, $5c$ , across the second expression, $(-4c + 5)$ .
This means we multiply $5c$ by each term in the second expression.
So, we have $5c \cdot (-4c) + 5c \cdot 5$ .

STEP 4

Calculating $5c \cdot (-4c)$ gives us $5 \cdot (-4) \cdot c \cdot c = -20c^2$ .
Remember, a negative times a positive is a negative!

STEP 5

Calculating $5c \cdot 5$ gives us $5 \cdot 5 \cdot c = 25c$ .

STEP 6

Now, let's distribute the second term of the first expression, $-8$ , across the second expression, $(-4c + 5)$ .
This gives us $-8 \cdot (-4c) + (-8) \cdot 5$ .

STEP 7

Calculating $-8 \cdot (-4c)$ gives us $-8 \cdot (-4) \cdot c = 32c$ .
A negative times a negative is a positive!

STEP 8

Calculating $-8 \cdot 5$ gives us $-40$ .

STEP 9

Putting it all together, we have $-20c^2 + 25c + 32c - 40$ .

STEP 10

We have two terms with just $c$ : $25c$ and $32c$ .
Let's combine them!

STEP 11

Adding $25c$ and $32c$ gives us $25c + 32c = (25 + 32)c = 57c$ .

STEP 12

So, our simplified expression is $-20c^2 + 57c - 40$ .

STEP 13

The product of $(5c - 8)$ and $(-4c + 5)$ is $-20c^2 + 57c - 40$ .

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