Question

If, in the expression $x^2-3$, x increases or decreases by a positive amount a, the expression changes by an amount

• A. $\pm 2ax+a^2$
• B. $2ax\pm a^2$
• C. $\pm a^2-3$
• D. $(x+a{)}^2-3$
• E. $(x-a{)}^2-3$

Answer 1

The correct option is A $\pm 2ax+a^2$

New expression, if x increases or decreases by a positive amount = ${(x\pm a)}^2-3$

Change in expression = $({(x\pm a)}^2-3)-(x^2-3)={(x\pm a)}^2-x^2=\pm 2ax+a^2$