Question

ПОЖАЛУЙСТО РЕШИТЕ, УМОЛЯЮ

Answer 1

Задание второе

$25a^2-10a+1=(5a-1)^2\ 64x^2-9y^2=(8x-3y)(8x+3y)\ 64x^3-27y^3=(4x)^3-(3y)^3=(4x-3y)(16x^2+12xy+9y^2)$
$b^5-b^3+b^2-1=b^3(b^2-1)+b^2-1=(b^2-1)(b^3+1)=\ =(b-1)(b+1)^2(b^2-b+1)$

Задание третье

$dfrac{43^2-17^2}{69^2-9^2} = dfrac{(43-17)(43+17)}{(69-9)(69+9)} = dfrac{26cdot 60}{60cdot 78} = dfrac{1}{3}$

$dfrac{14^2+28cdot 16+16^2}{15cdot 17+15cdot13} = dfrac{14^2+2cdot14cdot 16+16^2}{15cdot(17+13)} = dfrac{(14+16)^2}{15cdot30} = dfrac{30^2}{15cdot30} =2$

Answer 2

2)
a)
$25a^2-10a+1=(5a-1)^2=(5a-1)(5a-1)$
б)
$64x^2-9y^2=(8x)^2-(3y)^2=(8x-3y)(8x+3y)$
в)
$64x^3-27y^3=(4x)^3-(3y)^3=(4x-3y)(16x^2+12xy+9y^2)$
г)
$b^5-b^3+b^2-1=(b^5-b^3)+(b^2-1)=b^3(b^2-1)+(b^2-1)=$$=(b^2-1)(b^3+1)=(b-1)(b+1)(b+1)(b^2-b+1)=$$=(b-1)(b+1)^2(b^2-b+1)$

3)
а)
$frac{43^2-17^2}{69^2-9^2} = frac{(43-17)(43+17)}{(69-9)(69+9)} = frac{26*60}{60*78} = frac{26}{78}= frac{1}{3}$
б)
$frac{14^2+28*16+16^2}{15*17+15*13} = frac{14^2+2*14*16+16^2}{15(17+13)} = frac{(14+16)^2}{15*30} = frac{30^2}{15*30} = frac{30}{15} =2$