Question

, 7 клас. Без обьяснения, но с решением. В течении 40 минут))

Answer 1

$3ab^3-4a^3b-4a^2+3b^2=(3ab^3-4a^3b)+(3b^2-4a^2)=\\\\=ab(3b^2-4a^2)+(3b^2-4a^2)=(3b^2-4a^2)(ab+1)\\\\a=4\frac{1}{2}=\frac{9}{2} ,\; b=-\frac{2}{9}\\\\(3*(-\frac{2}{9})^2-4*(\frac{9}{2})^2)(\frac{9}{2}*(- \frac{2}{9})+1)=(\frac{3*4}{81}-\frac{4*81}{4})(-1+1)=(\frac{4}{27}-81)*0=0$

$k^2-8kp+7p^2=k^2-7kp-kp+7p^2=(k^2-7kp)-(kp-7p^2)=\\\\=k(k-7p)-p(k-7p)=(k-7p)(k-p)$

Answer 2

$\displaystyle 6)\ \ a=4\dfrac{1}{2}=\frac{9}{2}\ \ ,\ \ b=-\dfrac{2}{9}\\\\\\-3ab^3-4a^3b-4a^2+3b^2=-3b^2(ab+1)-4a^2(ab+1)=\\\\=(ab+1)(-3b^2-4a^2)=\Big(-\frac{9}{2}\cdot \frac{2}{9}+1\Big)\Big(3\cdot \frac{2^2}{9^2}-4\cdot \frac{9^2}{2^2}\Big)=0\\\\\\7)\ \ k^2-8kp+7p^2=(k^2-kp)+(-7kp+7p^2)=k(k-p)-7p(k-p)=\\\\=(k-p)(k-7p)$