Question

bonus: simplify and write in descending order. circle your final answer.
$2x-1+2x-1+2x-1+2x-1$
$(2x - 1)^4$
$8x^4-4$

Explanation:

Step1: Simplify the linear expression

Group like terms:
$(2x+2x+2x+2x) + (-1-1-1-1)$
$=8x - 4$

Step2: Expand the polynomial expression

First expand $(2x-1)^2$:
$(2x-1)^2=(2x)^2 - 2(2x)(1) + 1^2=4x^2-4x+1$
Then square the result for $(2x-1)^4$:
$(4x^2-4x+1)^2=(4x^2)^2 + (-4x)^2 + 1^2 + 2(4x^2)(-4x) + 2(4x^2)(1) + 2(-4x)(1)$
$=16x^4 + 16x^2 + 1 -32x^3 +8x^2 -8x$

Step3: Combine like terms for polynomial

Combine like terms from the expansion:
$16x^4 -32x^3 + (16x^2+8x^2) -8x +1$
$=16x^4 -32x^3 +24x^2 -8x +1$

Answer:

Simplified linear expression: $8x - 4$
Simplified polynomial expression (descending order): $16x^4 - 32x^3 + 24x^2 - 8x + 1$