B3:
a, $(a+1)^{2} - (a-1)^{2} - 3(a+1).(a-1)$
= $a^{2} + 2a + 1 - a^{2} + 2a - 1 -3a^{2} + 3$
= $-3a^{2}+4a +3$
b, $(m^{3}-m+1)^{2}+(m^{2}-3)^{2}-2(m^{2}-3)(m^{3}-m+1)$
= $(m^{3} - m + 1 - m^{2} + 3)^{2}$
= $(m^{3} - m^{2} - m + 4)^{2}$
B4:
a, $(5x +1)^{2} – (5x +3)(5x – 3) = 3$
⇔ $25x^{2} +10x + 1 - 25x^{2} + 9 =3$
⇔ $10x = -7$
⇔ $x = \frac{-7}{10}$
b, $(3x-5)(5-3x)+9(x+1)^{2}=30$
⇔ $-9x^{2} +30x - 25 + 9x^{2} +18x + 9 = 30$
⇔ $48x = 46$
⇔ $x = \frac{23}{24}$
c, $(x+4)^{2}-(x+1)(x-1)=16$
⇔ $x^{2} + 8x + 16 - x^{2} + 1 = 16$
⇔ $8x = -1$
⇔ $x = \frac{-1}{8}$