which expression is equivalent to 2(x - 1)^5+(x - 1)^6?\na. (x - 1)^5(x + 1)\nb. (x - 1)^6(2x - 1)\nc. 2(x…
which expression is equivalent to 2(x - 1)^5+(x - 1)^6?\na. (x - 1)^5(x + 1)\nb. (x - 1)^6(2x - 1)\nc. 2(x - 1)^5(x)\nd. 2(x - 1)^6(2x + 1)
Answer
Explanation:
Step1: Factor out common factor
Factor out ((x - 1)^5) from (2(x - 1)^5+(x - 1)^6). We know that ((x - 1)^6=(x - 1)^5\times(x - 1)). So, (2(x - 1)^5+(x - 1)^6=(x - 1)^5\times(2+(x - 1))).
Step2: Simplify the expression inside the parentheses
Simplify (2+(x - 1)). (2+(x - 1)=2 + x-1=x + 1). So the original expression is ((x - 1)^5(x + 1)).
Answer:
A. ((x - 1)^5(x + 1))