\(a,=\left(6x+1-6x+1\right)^2=4\\ b,=3x^2-6x-5x+5x^2-8x^2-24=-11x-24\\ c,=14x^2+x-3-5x^2-18x+8-9x^2+17x=5\\ d,=6x^2+43x-40-6x^2-7x+3-36x+27=-10\)

a) \(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2=\left(6x+1-6x+1\right)^2=2^2=4\)

b) \(=3x^2-6x-5x+5x^2-8x^2+24=-11x+24\)

c) \(\left(7x-3\right)\left(2x+1\right)-\left(5x-2\right)\left(x+4\right)-9x^2+17x=\left(7x-3\right).2x+\left(7x-3\right)-\left[\left(5x-2\right).x+4\left(5x-2\right)\right]-9x^2+17x=14x^2-6x+7x-3-\left(5x^2-2x+20x-8\right)-9x^2+17x=5x^2+18x-3-\left(5x^2+18x-8\right)=5x^2+18x-3-5x^2-18x+8=5\)

d) \(\left(6x-5\right)\left(x+8\right)-\left(3x-1\right)\left(2x+3\right)-9\left(4x-3\right)=\left(6x-5\right).x+8\left(6x-5\right)-\left[\left(3x-1\right).2x+3\left(3x-1\right)\right]-36x+27=6x^2-5x+48x-40-\left(6x^2-2x+9x-3\right)-36x+27=6x^2+7x-13-\left(6x^2+7x-3\right)=6x^2+7x-13-6x^2-7x+3=-10\)

Bài 1:

a) \(=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1=\left(x+1\right)\left(x+3\right)\)

f) \(=\left(x^2-4x+4\right)-9=\left(x-2\right)^2-3^2=\left(x-5\right)\left(x+1\right)\)

h) \(=x^2\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)

k) \(=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left(x^3-x-1\right)\)

m) \(=\left(x^4+4x^2+4\right)-9=\left(x^2+2\right)^2-9=\left(x^2-1\right)\left(x^2+5\right)=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

Bài 2:

a) \(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)

e) \(=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

f) giống câu a

g) \(=x^2-2xy=x\left(x-2y\right)\)

i) \(=\left(x^3-y^3\right)\left(x^3+y^3\right)=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

k) \(=\left(x+1\right)^3-27z^3=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)

l) \(=\left(2x+1\right)^2-9y^2=\left(2x+1-3y\right)\left(2x+1+3y\right)\)

Em đăng tách ra 1 lần 5-7 câu thôi he!

1:

(SAB), (SBC) vuông góc (BAC)

=>SB vuông góc (ABC)

AC vuông góc AB,SB

=>AC vuông góc (SAB)

=>AC vuông góc BH

mà SA vuông góc BH

nên BH vuông góc (SAC)

=>BH vuông góc SC

mà SC vuông góc BK

nên SC vuông góc (BHK)

c: (SH;(BHK))=góc SHK=(SA;BHK)

BC=BA/cos60=2a

SC=căn SB^2+BC^2=ăcn 5

SB^2=SK*SC

=>SK=a*căn 5/5

SA=căn SB^2+AB^2=a*căn 2

SB^2=SH*SA

=>SH=a*căn 2/2

sin SHK=căn 10/5

=>góc SHK=39 độ

câu 9 bài IV chọn B are communicated => communicate 

a.

Ta có: MN//BC (gt)

Áp dụng định lý Ta-lét, ta có:

\(\dfrac{AM}{AB}=\dfrac{AN}{AC}\)

\(\Leftrightarrow\dfrac{1,2}{3}=\dfrac{AN}{4}\)

\(\Leftrightarrow3AN=4,8\)

\(\Leftrightarrow AN=1,6cm\)

b.Áp dụng định lý pitago vào tam giác vuông ABC, có:

\(BC^2=AB^2+AC^2\)

\(\Rightarrow BC=\sqrt{3^2+4^2}=\sqrt{25}=5cm\)

Áp dụng t/c đường phân giác góc A, ta có:

\(\dfrac{AB}{AC}=\dfrac{BD}{CD}\)

\(\Leftrightarrow\dfrac{3}{4}=\dfrac{BD}{CD}\)

\(\Leftrightarrow\dfrac{CD}{4}=\dfrac{BD}{3}\)

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\dfrac{CD}{4}=\dfrac{BD}{3}=\dfrac{CD+BD}{4+3}=\dfrac{5}{7}\)

\(\Rightarrow CD=\dfrac{5}{7}.4=\dfrac{20}{7}cm\)

\(\Rightarrow BD=\dfrac{5}{7}.3=\dfrac{15}{7}cm\)