Question

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ecc5d012fb4b0f7491bcf33cd8823049.txt

Answer 1

Ответ:

$a^2-9=(a-3)(a+3)\\\\b^2+1=(b^2+2b+1)-2b=(b+1)^2-2b=(b+1-\sqrt{2b})(b+1+\sqrt{2b})\\\\4-c^2=(2-c)(2+c)\\\\25+x^2=(25+10x+x^2)-10x=(x+5)^2-10x=(x+5-\sqrt{10x})(5+x+\sqrt{10x})\\\\1-y^2=(1-y)(1+y)$

$16a^2-b^2=(4a-b)(4a+b)\\\\81+100p^2=(81+100p^2+180p)-180p=(9+10p)^2-180p=\\\\=(8+10p-6\sqrt{5p})(8+10p+6\sqrt{5p})\\\\81-100p^2=(9-10p)(9+10p)\\\\m^2n^2-25=(mn-5)(mn+5)\\\\-m^2n^2-25=-\Big((m^2n^2+25+10mn)-10mn\Big)=10mn-(mn+5)^2=\\\\=(\sqrt{10mn}-mn-5)(\sqrt{10mn}+mn+5)$