Đáp án:
$a) m^3n^3+5mn^2-m^2n-5\\
b) 16x^4-1\\
c) -37\\
d) t^4-16$
Giải thích các bước giải:
$a) (mn^2-1) . (m^2n+5)\\
=mn^2 . (m^2n+5)-1 . (m^2n+5)\\
=mn^2.m^2n+mn^2.5-m^2n-5\\
=m^3n^3+5mn^2-m^2n-5\\
b) 4(x-1/2) . (x+1/2).(4x^2+1)\\
=4.\left [x^2-\left (\dfrac{1}{2} \right )^2 \right ].(4x^2+1)\\
=4.\left ( x^2-\dfrac{1}{4} \right ).(4x^2+1)\\
=4.\dfrac{1}{4}.(4x^2-1).(4x^2+1)\\
=(4x^2)^2-1\\
=16x^4-1\\
c) (m^2-2m+4) . (m+2)-m^3+(m+3) . (m-3)-m^2-18\\
=(m+2)(m^2-2m+4)-m^3+m^2-3^2-m^2-18\\
=m^3+2^3-m^3+m^2-27-m^2-18\\
=(m^3-m^3)+(m^2-m^2)+(-27-18+2^3)\\
=-37\\
d) [(t+2) . (t^2+4)] . (t-2)\\
=(t+2).(t-2).(t^2+4)\\
=(t^2-4)(t^2+4)\\
=(t^2)^2-4^2\\
=t^4-16$
