Giải bài 1 trang 13 SBT Toán 8 tập 1 CTST

a) $(4x – 5)^{2} = (4x)^{2} ‒ 2.4x.5 + 5^{2} = 16x^{2} ‒ 40x + 25.$

b)$ (3x + \frac{1}{3}y)^{2}$

$= (3x)^{2} + 2.3x.\frac{1}{3}y+ (\frac{1}{3}y)^{2}$

$= 9x^{2} + 2xy + \frac{1}{9}y^{2}$

c) $(–x + 0,3)2 = (‒x)^{2} + 2.(‒x).0,3 + 0,3^{2} = x^{2} ‒ 0,6x + 0,09.$

d)$ (–x – 10y)^{2} = (‒x)^{2} + 2.(‒x).(‒10y) + (‒10y)^{2}$

$= x^{2} + 20xy + 100y^{2}.$

e)$(a^{3} – 3a)^{2} = (a^{3})^{2} ‒ 2.a^{3}.3a + (3a)^{2}$

$= a^{6} + 6a^{4} + 9a^{2}$.

g)$(a^{4} + \frac{1}{2}a^{2})^{2}$

$= (a^{4})^{2} + 2.a^{4}.\frac{1}{2}a^{2}+(\frac{1}{2}a^{2})^{2}$

$= a^{8} + a^{6}+ \frac{1}{4}$