Hoàn thiện HĐT ta thu được các đơn thức cần điền vào “…”.

a)  x 2 + 4x + 4 = ( x   +   2 ) 2 .           b) 4 x 2 – 12x + 9 = ( 2 x   –   3 ) 2 .

c) 4 x 2  – 12xy + 9 y 2 = ( 2 x   –   3 y ) 2 .

Chú ý: phép trừ ta chuyển thành cộng đại số.

d)  x − y 2 x + y 2 = x 2 − y 2 4 .

a: \(x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\)

b: \(4x^2-4x+1=\left(2x\right)^2-2\cdot2x\cdot1+1^2=\left(2x-1\right)^2\)

c: \(2x-1-x^2\)

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

d: \(x^2+x+\dfrac{1}{4}=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)

e: \(9-x^2=3^2-x^2=\left(3-x\right)\left(3+x\right)\)

g: \(\left(x+5\right)^2-4x^2=\left(x+5+2x\right)\left(x+5-2x\right)\)

\(=\left(5-x\right)\left(5+3x\right)\)

h: \(\left(x+1\right)^2-\left(2x-1\right)^2\)

\(=\left(x+1+2x-1\right)\left(x+1-2x+1\right)\)

\(=3x\left(-x+2\right)\)

i: \(=x^2y^2-4xy+4-3\)

\(=\left(xy-2\right)^2-3=\left(xy-2-\sqrt{3}\right)\left(xy-2+\sqrt{3}\right)\)

k: \(=y^2-\left(x-1\right)^2\)

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

l: \(=x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=\left(x+2\right)^3\)

m: \(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3=\left(2x-y\right)^3\)

a)
=(x-2)³
b)\(\left(2-x\right)^3\)
c)\(\left(x+\dfrac{1}{3}\right)^3\)
d)\(\left(\dfrac{x}{2}+y\right)^3\)
e)
\(=\left(x-1\right)^2\left(x-1-15\right)+25\left[3\left(x-1\right)-5\right]\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-3-5\right)\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-8\right)\)
 

a,= (x+4)\(^3\)

b,= (x-2)\(^3\)

c,= x\(^3\)+8

d,=x\(^3\)-27

a,= x\(^3\)+3.4x\(^2\)+3.4\(^2\).x+4\(^3\)=(x+4)\(^3\)

-3.2.x\(^2\)+3.2\(^2\).x-2\(^3\)= (x-2)\(^3\)

còn c,d áp dụng HĐT là ra! ( đc chx bà nội)

1) \(\left(\dfrac{1}{2}x+3\right)\left(x^2-4x-6\right)\)

\(=\dfrac{1}{2}x^3-2x^2-3x+3x^2-12x-18\)

\(=\dfrac{1}{2}x^3+x^2-15x-18\)

2) \(\left(6x^2-9x+15\right)\left(\dfrac{2}{3}x+1\right)\)

\(=4x^3+6x^2-6x^2-9x+10x+15\)

\(=4x^3+x+15\)

3) Ta có: \(\left(3x^2-x+5\right)\left(x^3+5x-1\right)\)

\(=3x^5+15x^2-3x^2-x^4-5x^2+x+5x^3+25x-5\)

\(=3x^5-x^4+5x^3+10x^2+26x-5\)

4) Ta có: \(\left(x-1\right)\left(x+1\right)\left(x-2\right)\)

\(=\left(x^2-1\right)\left(x-2\right)\)

\(=x^3-2x^2-x+2\)

a) \(x^2+4x+4=\left(x+2\right)^2\)

b) \(x^2-8x+16=\left(x-4\right)^2\)

c) \(\left(x+5\right)\left(x-5\right)=x^2-25\)

g) \(\left(x-2\right)\left(x^2-2x+4\right)\)

\(=x^3-8\)

a) \(=\left(x+2\right)^2\)

b) \(=\left(x-4\right)^2\)

c) \(=x^2-25\)

g) \(=x^3-8\)

a) x² + 4x + 4 = ( x + 2 )²

b) x² - 8x + 16 = ( x - 4 )²

c) ( x + 5 ) . ( x - 5 ) = x² - 5²

Câu 1. D

Câu 4. A, C

Câu 5. Xem lại đề!

Câu 5. D

Câu 7. B

Câu 8. A

Bạn không hiểu chỗ nào cứ hỏi lại mình nhé!

a) x = -1.                      b) x = 4 hoặc x = 5.

c) x = ± 2 .                  d) x = 1 hoặc x = 2.