Problem: If, in the expression x2−3x^{2}-3x2−3, xxx increases or decreases by a positive amount aaa, the expression changes by an amount:
Answer Choices:
A. ±2ax+a2\pm 2 \mathrm{ax}+\mathrm{a}^{2}±2ax+a2
B. 2ax±a22 a x \pm a^{2}2ax±a2
C. ±a2−3\pm a^{2}-3±a2−3
D. (x+a)2−3(x+a)^{2}-3(x+a)2−3
E. (x−a)2−3(x-a)^{2}-3(x−a)2−3 Solution:
y1=x2−3y_{1}=x^{2}-3 y1=x2−3
y2=(x±a)2−3y_{2}=(x \pm a)^{2}-3 y2=(x±a)2−3
y2−y1=±2ax+a2y_{2}-y_{1}= \pm 2 a x+a^{2} y2−y1=±2ax+a2