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a) (3+\(xy^2\))\(^2\)= \(3^2\)+2*3*\(xy^2\)+\(\left(xy^2\right)\)\(^2\)
=9+6\(xy^2\)+\(x^2\)\(y^4\)
b) (a+\(b^2\))(a-\(b^2\))
=a(a-\(b^2\))+\(b^2\)(a-\(b^2\))
=a*a+a*-\(b^2\)+\(b^2\)*a+\(b^2\)*-\(b^2\)
=\(a^2\)-a\(b^2\)+\(b^2\)a-\(b^4\)
=\(a^2\)+(-a\(b^2\)+a\(b^2\))-\(b^4\)
=\(a^2\)-\(b^4\)
c)(2y-1)\(^2\)=(2y)\(^2\)-2*2y*1+1\(^{^2}\)
=4y\(^2\)-4y+1
d)(10-m\(^2\))\(^2\)=10\(^2\)-2*10*m\(^2\)+(m\(^2\))\(^2\)
=100-20m\(^2\)+m\(^4\)
câu e bạn tự làm nha tương tự như câu b
chúc bạn học tốt
a) \(\left(3-xy^2\right)^2-\left(2+xy^2\right)^2\)
\(=\left(3-xy^2-2-xy^2\right)\left(3-xy^2+2+xy^2\right)\)
\(=\left(1-2xy^2\right).5=5-10xy^2\)
b) \(9x^2-\left(3x-4\right)^2\)
\(=\left(3x-3x+4\right)\left(3x+3x-4\right)\)
\(=4.\left(6x-4\right)=24x-16\)
c) \(\left(a-b^2\right)\left(a+b^2\right)\)
\(=a^2-b^{^4}\)
d) \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)
\(=\left[\left(a^2+2a\right)^2\right]-3^2\)
\(=a^4+4a^3+4a^2-9\)
h) Sửa lại đề bài chút xíu:
$(xy+ab)^2+(ay-bx)^2=x^2y^2+a^2b^2+2abxy+a^2y^2-2aybx+b^2x^2$
$=x^2y^2+a^2b^2+a^2y^2+b^2x^2$
$=(x^2y^2+b^2x^2)+(a^2b^2+a^2y^2)$
$=x^2(y^2+b^2)+a^2(b^2+y^2)=(a^2+x^2)(b^2+y^2)$
j)
$ab(x^2+y^2)+xy(a^2+b^2)=abx^2+aby^2+xya^2+xyb^2$
$=(abx^2+xya^2)+(aby^2+xyb^2)$
$=ax(bx+ay)+by(ay+bx)=(ax+by)(ay+bx)$
k)
$(xy-ab)^2+(bx+ay)^2=x^2y^2-2xyab+a^2b^2+b^2x^2+2bxay+a^2y^2$
$=x^2y^2+a^2b^2+b^2x^2+a^2y^2$
$=(x^2y^2+b^2x^2)+(a^2b^2+a^2y^2)=x^2(y^2+b^2)+a^2(b^2+y^2)$
$=(a^2+x^2)(b^2+y^2)$
e)
$x^2-(2a+b)xy+2aby^2=x^2-2axy-bxy+2aby^2$
$=x(x-2ay)-by(x-2ay)=(x-by)(x-2ay)$
g)
$y^2-(3a+2b)xy+6abx^2=(y^2-2bxy)-(3axy-6abx^2)$
$=y(y-2bx)-3ax(y-2bx)=(y-3ax)(y-2bx)$
f)
$3xy(a^2+b^2)-ab(x^2+9y^2)=3xya^2+3xyb^2-abx^2-9aby^2$
$=(3xya^2-abx^2)-(9aby^2-3xyb^2)$
$=ax(3ay-bx)-3by(3ay-bx)=(3ay-bx)(ax-3by)$
a) \(\left(3+xy^2\right)^2=9+6xy^2+x^2y^4\)
b) \(\left(10-2m^2n\right)^2=100-40m^2n+4m^4n^2\)
c) \(\left(a-b^2\right)\left(a+b^2\right)=a^2-\left(b^2\right)^2=a^2-b^4\)
e) \(\left(xy-1\right)^3=x^3y^3-3x^2y^2+3xy-1\)