Step-By-Step Solution:
To simplify the expression [tex]-rxt - 8r^2x+3x^2-6rx^2[/tex], you need to combine like terms and rewrite it in standard form, which is a polynomial arranged in descending exponents order.
1. First, group the like terms:
[tex]-rxt[/tex] and [tex]-8r^2x[/tex] are like terms as they both have a factor of [tex]x[/tex], but their coefficients are different.
[tex]-6rx^2[/tex] and [tex]3x^2[/tex] are like terms as they both have a factor of [tex]3x^2[/tex], but again their coefficients are different.
2. Next, combine the like terms:
[tex]-rxt - 8r^2x = -(rx + 8r^2x) = -rx(1 + 8r)[/tex]
[tex]3x^2 - 6rx^2 = x^2(3 - 6r)=3x^2(1-2r)[/tex]
3. Now, rewrite the expression in standard form:
[tex]-rx(1 + 8r) + 3x^2(1 - 2r) = -rx - 8r^2x + 3x^2 - 6rx^2 = 3x^2 - 6rx^2 - rx - 8r^2x[/tex]
Therefore, the simplified expression in standard form is [tex]3x^2 - 6rx^2 - rx - 8r^2x[/tex].
Answer:
[tex]3x^2 - 6rx^2 - rx - 8r^2x[/tex]
