Giúp mũi làm bài tập và ập mị cảm ơn nhiều ạ
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b.
\(6x^2-12x+6=6\left(x^2-2x+1\right)\)
\(=6\left(x-1\right)^2\)
c.
\(4x^2-20x+25\)
\(=\left(2x-5\right)^2\)
d. Câu này đề sai
e.
\(x^5-x^3+x^2-1\)
\(=x^3\left(x^2-1\right)+x^2-1\)
\(=\left(x^2-1\right)\left(x^3+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)^2\left(x^2-x+1\right)\)
Bài 17:
1) \(3^2-x^2=\left(3-x\right)\left(3+x\right)\)
2) \(x^2-36=\left(x-6\right)\left(x+6\right)\)
3) \(y^2-1=\left(y-1\right)\left(y+1\right)\)
4) \(25-y^2=\left(5-y\right)\left(5+y\right)\)
5) \(9x^2-1=\left(3x-1\right)\left(3x+1\right)\)
6) \(\dfrac{1}{25}-4x^2=\left(\dfrac{1}{5}-2x\right)\left(\dfrac{1}{5}+2x\right)\)
7) \(9x^2-y^2=\left(3x-y\right)\left(3x+y\right)\)
8) \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
Bài 18:
1) \(\left(x-5\right)\left(x+5\right)=x^2-25\)
2) \(\left(4-x\right)\left(4+x\right)=16-x^2\)
3) \(\left(x-\dfrac{2}{3}\right)\left(x+\dfrac{2}{3}\right)=x^2-\dfrac{4}{9}\)
4) \(\left(1+2x\right)\left(1-2x\right)=1-4x^2\)
5) \(-\left(2x+3\right)\left(3-2x\right)=\left(2x+3\right)\left(2x-3\right)=4x^2-9\)
6) \(-\left(5x-3\right)\left(3+5x\right)=\left(3-5x\right)\left(3+5x\right)=9-25x^2\)
7) \(-\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)=-\left(9x^2-\dfrac{4}{25}\right)=\dfrac{4}{25}-9x^2\)
8) \(-\left(2x-\dfrac{2}{3}\right)\left(2x+\dfrac{2}{3}\right)=-\left(4x^2-\dfrac{4}{9}\right)=\dfrac{4}{9}-4x^2\)
Bài 3.
a. Ta có: \(CK=BK\left(gt\right)\Rightarrow OK\perp BC\)
Ta có: \(\widehat{OIC}=90^o\)
\(\widehat{OKC}=90^o\)
\(\Rightarrow\widehat{OIC}+\widehat{OKC}=90^o+90^o=180^o\)
`=>` Tứ giác CIOK nội tiếp đường tròn
b. Xét \(\Delta AID\) và \(\Delta CIB\), có:
\(\widehat{AID}=\widehat{CIB}=90^o\left(gt\right)\)
\(\widehat{ADI}=\widehat{CBI}\) ( cùng chắn \(\stackrel\frown{AC}\) )
Vậy \(\Delta AID\sim\Delta CIB\) ( g.g)
\(\Rightarrow\dfrac{IA}{IC}=\dfrac{ID}{IB}\)
\(\Leftrightarrow IC.ID=IA.IB\)
c. Kẻ \(DM\perp AC\)
Ta có: \(\widehat{ACB}=90^o\) ( góc nt chắn nửa đtròn )
`->` Tứ giác DMCK là hình chữ nhật
\(\rightarrow DK\perp BC\)
Mà \(OK\perp BC\)
\(\Rightarrow\) 3 điểm D,O,K thẳng hàng
games: computer games, chess, blind man's buff trò chơi: trò chơi điện tử, cờ vua, bịt mắt bắt dê
sports: football, gymnastics, aerobics thể thao: bóng đá, thể dục dụng cụ, thể dục nhịp điệu
arts and crafts: pottery, painting, making handmade flowers nghệ thuật và thủ công: gốm, vẽ tranh, làm hoa thủ công
other activities: swimming, sleeping, watching TV các hoạt động khác: bơi lội, ngủ, xem TV
1 interested in travelling by plane
2 15 minutes riding his bike to school
3 is made by my mother everymorning
4 take care of her little brother
5 able to speak 2 languages when he was young
6 able to play the piano
7 is played all over VN
8 to play voleyball very well when he was young
9 to go fishing when he was young
10 way to the shopping mall
over
camping
was
couldn't
percussion
takes
look after
go around
go through
wind
how long
for
do










Bài 5:
a: \(x^2-7x+6\)
\(=x^2-x-6x+6\)
=x(x-1)-6(x-1)
=(x-1)(x-6)
b: \(x^2-6x+3\)
\(=x^2-6x+9-6\)
\(=\left(x-3\right)^2-6=\left(x-3-\sqrt6\right)\left(x-3+\sqrt6\right)\)
c: \(x^2-4x+3\)
\(=x^2-x-3x+3\)
=x(x-1)-3(x-1)
=(x-1)(x-3)
d: \(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
=3x(x-1)-2(x-1)
=(x-1)(3x-2)
e: \(7x^2-x-6\)
\(=7x^2-7x+6x-6\)
=7x(x-1)+6(x-1)
=(x-1)(7x+6)
f: \(3x^2-5x-8\)
\(=3x^2-8x+3x-8\)
=x(3x-8)+(3x-8)
=(3x-8)(x+1)
g: \(x^2-6x+5\)
\(=x^2-x-5x+5\)
=x(x-1)-5(x-1)
=(x-1)(x-5)
h: \(x^2-2x-3\)
\(=x^2-3x+x-3\)
=(x-3)(x+1)
i: \(x^2-x-12\)
\(=x^2-4x+3x-12\)
=x(x-4)+3(x-4)
=(x-4)(x+3)
j: \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
=x(x-2y)-5y(x-2y)
=(x-2y)(x-5y)
k: \(x^2+6xy+5y^2\)
\(=x^2+xy+5xy+5y^2\)
=x(x+y)+5y(x+y)
=(x+y)(x+5y)
l: \(3x^2-4xy+y^2\)
\(=3x^2-3xy-xy+y^2\)
=3x(x-y)-y(x-y)
=(x-y)(3x-y)
m: \(x^2-xy-6y^2\)
\(=x^2-3xy+2xy-6y^2\)
=x(x-3y)+2y(x-3y)
=(x-3y)(x+2y)
Bài 4:
a: \(5a^2+10ab+5b^2\)
\(=5\left(a^2+2ab+b^2\right)=5\left(a+b\right)^2\)
b: \(6x^2-12x+6\)
\(=6\left(x^2-2x+1\right)\)
\(=6\left(x-1\right)^2\)
c: \(4x^2-20x+25\)
\(=\left(2x\right)^2-2\cdot2x\cdot5+5^2\)
\(=\left(2x-5\right)^2\)
e: \(x^5-x^3+x^2-1\)
\(=x^3\cdot\left(x^2-1\right)+\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^3+1\right)=\left(x+1\right)^2\cdot\left(x-1\right)\left(x^2-x+1\right)\)
f: \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-9\)
=(x-y-3)(x-y+3)
h: \(1-x^2+2xy-y^2\)
\(=1-\left(x^2-2xy+y^2\right)\)
\(=1-\left(x-y\right)^2=\left(1-x+y\right)\left(1+x-y\right)\)
k: \(4x^2-1+y^2-4xy\)
\(=\left(4x^2-4xy+y^2\right)-1\)
\(=\left(2x-y\right)^2-1\)
=(2x-y-1)(2x-y+1)
l: \(-x^2-2xy-y^2+4\)
\(=4-\left(x^2+2xy+y^2\right)\)
\(=2^2-\left(x+y\right)^2\)
=(2-x-y)(2+x+y)
m: \(3x^3+6x^2y+3xy^2\)
\(=3x\left(x^2+2xy+y^2\right)\)
\(=3x\left(x+y\right)^2\)
n: \(20x^2+20xy+5y^2\)
\(=5\cdot\left(4x^2+4xy+y^2\right)\)
\(=5\left(2x+y\right)^2\)