How do you simplify (2+sqrtx)(8+sqrtx)(2+√x)(8+√x)?

1 Answer
Jim G.
Jan 23, 2017

16+10sqrtx+x16+10√x+x

Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket. This can be achieved as follows.

rArr(color(red)(2+sqrtx))(8+sqrtx)⇒(2+√x)(8+√x)

=color(red)(2)(8+sqrtx)color(red)(+sqrtx)(8+sqrtx)=2(8+√x)+√x(8+√x)

distribute the brackets.

rArr16+2sqrtx+8sqrtx+(sqrtx xxsqrtx)⇒16+2√x+8√x+(√x×√x)

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(sqrtx xxsqrtx=x)color(white)(2/2)|)))

collecting like terms and simplifying.

=16+10sqrtx+x

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