Question

1. write a simplified algebraic expression for the following: image of tiles: -x (red rectangle), -x² (brown square), -x (red rectangle), -x (red rectangle), -x² (brown square)

Explanation:

Step1: Identify like terms

We have two types of terms: terms with $x^2$ and terms with $x$. The terms with $x^2$ are $-x^2$ and $-x^2$, and the terms with $x$ are $-x$, $-x$, and $-x$.

Step2: Combine like terms for $x^2$

To combine the $x^2$ terms, we add their coefficients. The coefficient of $-x^2$ is $-1$, so for two $-x^2$ terms: $(-1)x^2 + (-1)x^2 = (-1 - 1)x^2 = -2x^2$.

Step3: Combine like terms for $x$

To combine the $x$ terms, we add their coefficients. The coefficient of $-x$ is $-1$, so for three $-x$ terms: $(-1)x + (-1)x + (-1)x = (-1 - 1 - 1)x = -3x$.

Step4: Combine the results

Now we combine the combined $x^2$ terms and the combined $x$ terms to get the simplified expression: $-2x^2 - 3x$.

Answer:

$-2x^2 - 3x$