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Aus Online Mathematik Brückenkurs 1

We expand the first product of bracketed terms by multiplying each term inside the first bracket by each term from the second bracket

(1−5x)(1+15x)=11+115x−5x1−5x15x=1+15x−5x−75x2=1+10x−75x2.

As for the second expression, we can use the conjugate rule (a−b)(a+b)=a2−b2 where a=2 and b=5x,

3(2−5x)(2+5x)=322−(5x)2=3(4−25x2)=12−75x2.

All together, we obtain

(1−5x)(1+15x)−3(2−5x)(2+5x)=(1+10x−75x2)−(12−75x2)=1+10x−75x2−12+75x2=1−12+10x−75x2+75x2=−11+10x.