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Bài 2:
a) \(\left(x+5\right)^2=x^2+10x+25\)
b) \(\left(\dfrac{5}{2}-t\right)^2=\dfrac{25}{4}-5t+t^2\)
c) \(\left(2u+3v\right)^2=4u^2+12uv+9v^2\)
d) \(\left(-\dfrac{1}{8}a+\dfrac{2}{3}bc\right)^2=\dfrac{1}{64}a^2-\dfrac{1}{6}abc+\dfrac{4}{9}b^2c^2\)
e) \(\left(\dfrac{x}{y}-\dfrac{1}{z}\right)^2=\dfrac{x^2}{y^2}-\dfrac{2x}{yz}+\dfrac{1}{z^2}\)
f) \(\left(\dfrac{mn}{4}-\dfrac{x}{6}\right)\left(\dfrac{mn}{4}+\dfrac{x}{6}\right)=\dfrac{m^2n^2}{16}-\dfrac{x^2}{36}\)
Bài 1:
$M=(2a+b)^2-(b-2a)^2=[(2a+b)-(b-2a)][(2a+b)+(b-2a)]$
$=4a.2b=8ab$
$N=(3a+1)^2+2a(1-2b)+(2b-1)^2$
$=(9a^2+6a+1)+2a-4ab+(4b^2-4b+1)$
$=9a^2+8a+4b^2-4b-4ab+2$
$A=(m-n)^2+4mn=m^2-2mn+n^2+4mn$
$=m^2+2mn+n^2=(m+n)^2$
a: =(5a-a+b)(5a+a-b)
=(4a+b)(5a-b)
b: =(2a-a-b)(2a+a+b)
=(a-b)(3a+b)
c: =(7a-2a+b)(7a+2a-b)
=(5a+b)(9a-b)
d: =(6a-3a+2b)(6a+3a-2b)
=(3a+2b)(9a-2b)
e: =(9a-5a+3b)(9a+5a-3b)
=(4a+3b)(14a-3b)
Lời giải:
$25a^2-(a-b)^2=(5a)^2-(a-b)^2=[5a-(a-b)][5a+(a-b)]=(4a+b)(6a-b)$
$4a^2-(a+b)^2=(2a)^2-(a+b)^2=[2a-(a+b)][2a+(a+b)]=(a-b)(3a+b)$
$49a^2-(2a-b)^2=(7a)^2-(2a-b)^2=[7a-(2a-b)][7a+(2a-b)]=(5a+b)(9a-b)$
$36a^2-(3a-2b)^2=(6a)^2-(3a-2b)^2=[6a-(3a-2b)][6a+(3a-2b)]$
$=(3a+2b)(9a-2b)$
$81a^2-(5a-3b)^2=(9a)^2-(5a-3b)^2=[9a-(5a-3b)][9a+(5a-3b)]$
$=(4a+3b)(14a-3b)$
a) \(\left(2a-b\right)\left(b+4a\right)+2a\left(b-3a\right)\)
\(=2ab+8a^2-b^2-4ab+2ab-6a^2\)
\(=\left(2ab+2ab-4ab\right)+\left(8a^2-6a^2\right)-b^2\)
\(=2a^2-b^2\)
b) \(\left(3a-2b\right).\left(2a-3b\right)-6a\left(a-b\right)\)
\(=6a^2-9ab-4ab+6b^2-6a^2+6ab\)
\(=\left(6a^2-6a^2\right)-\left(9ab+4ab-6ab\right)+6b^2\)
\(=-7ab+b^2\)
c) \(5b\left(2x-b\right)-\left(8b-x\right)\left(2x-b\right)\)
\(=10bx-5b^2-\left(16bx-8b^2-2x^2+bx\right)\)
\(=10bx-5b^2-16bx+8b^2+2x^2-bx\)
\(=\left(10bx-16bx-bx\right)-\left(5b^2-8b^2\right)+2x^2\)
\(=-7bx+3b^2+2x^2\)
d) \(2x\left(a+15x\right)+\left(x-6a\right)\left(5a+2x\right)\)
\(=2ax+30x^2+5ax+2x^2-30a^2-12ax\)
\(=\left(2ax+5ax-12ax\right)+\left(30x^2+2x^2\right)-30a^2\)
\(=-5ax+32x^2-30a^2\)
a: =2ab+8a^2-b^2-4ab+2ab-6a^2
=2a^2-b^2
b: =6a^2-9ab-4ab+6b^2-6a^2+6ab
=-7ab+6b^2
c: =10bx-5b^2-16bx+8b^2+2x^2-xb
=3b^2+2x^2-7xb
d: =2xa+30x^2+5ax+2x^2-30a^2-12ax
=32x^2-30a^2-5ax
Bài 1:
\(\frac{15ab+5b^2}{9a^2-b^2}=\frac{5b\left(3a+b\right)}{\left(3a\right)^2-b^2}=\frac{5b\left(3a+b\right)}{\left(3a-b\right)\left(3a+b\right)}=\frac{5b}{3a-b}\)
\(\frac{3x^2-3y^2}{9x+9y}=\frac{3\left(x^2-y^2\right)}{9\left(x+y\right)}=\frac{\left(x-y\right)\left(x+y\right)}{3\left(x+y\right)}=\frac{x-y}{3}\)
\(\frac{m^2-4m+4}{2x-4}=\frac{\left(x-2\right)^2}{2\left(x-2\right)}=\frac{x-2}{2}\)