Question1. $(2 x-6)(x+11)$

Studdy Solution

STEP 1

What is this asking? We need to expand this expression, which means multiplying these two things together! Watch out! Don't forget to multiply every term in the first parentheses by every term in the second parentheses.
It's easy to miss one!

STEP 2

1. Distribute the terms
2. Simplify

STEP 3

Let's start by multiplying $2x$ by both terms in the second parentheses, $x + 11$ .
$2x \cdot x = 2x^2$ $2x \cdot 11 = 22x$ So, the first part of our expansion is $2x^2 + 22x$ .

STEP 4

Now, we'll multiply $-6$ by both terms in the second parentheses, $x + 11$ .
$-6 \cdot x = -6x$ $-6 \cdot 11 = -66$ This gives us $-6x - 66$ .

STEP 5

Putting it all together, we have $2x^2 + 22x - 6x - 66$ .

STEP 6

Notice we have two terms with just an $x$ : $22x$ and $-6x$ .
Let's combine them!
$22x - 6x = 16x$

STEP 7

Now, we can rewrite the entire expression in its simplified form: $2x^2 + 16x - 66$ .
Look at that, nice and neat!

STEP 8

The expanded and simplified form of $(2x - 6)(x + 11)$ is $2x^2 + 16x - 66$ .

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