a) (x + 3)² - 2(x + 3)(x - 2) + (x - 2)² 

= (x + 3 - x + 2)² = 5² = 25

b) (2x + 5)² + 2(2x + 5)(3x - 1) + (3x - 1)² 

= (2x  + 5 + 3x - 1)² = (5x  + 4)²

Trả lời:

a/ ( x + 3 )² - 2 ( x + 3 ) ( x - 2 ) + ( x - 2 )²

=  [ ( x + 3 ) - ( x - 2 ) ]² 

= ( x + 3 - x + 2 )²

= 5²

= 25

b/ ( 2x + 5 )² + 2 ( 2x + 5 ) ( 3x - 1 ) + ( 3x - 1 )²

= ( 2x + 5 + 3x - 1 )²

= ( 5x + 4 )²

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 .

Ta có:\(TH1:\left(3x+1\right)^2-\left(1-2x\right)^2=\left(3x+1+1-2x\right)\left(3x+1-1+2x\right)=\left(x+2\right)\left(5x\right)\)

            Còn ra hằng đẳng thức thì mk chịu

\(a,a^2y^2+b^2x^2-2abxy\\ =\left(ay\right)^2-2abxy+\left(bx\right)^2\\ =\left(ay-bx\right)^2=\left(bx-ay\right)^2\\ ---\\ b,100-\left(3x-y\right)^2\\ =10^2-\left(3x-y\right)^2\\ =\left(10-3x+y\right)\left(10+3x-y\right)\)

a) \(=\left(ay\right)^2-2abxy+\left(bx\right)^2\)

\(=\left(ay-bx\right)^2\)

b) \(100-\left(3x-y\right)^2\)

\(=10^2-\left(3x-y\right)^2\)

\(=\left(10-3x+y\right)\left(10+3x-y\right)\)

\(x^2+3x-10\)

\(=x^2+5x-2x-10\)

\(=\left(x^2+5x\right)-\left(2x+10\right)\)

\(=x\left(x+5\right)-2\left(x+5\right)\)

\(=\left(x-2\right)\left(x+5\right)\)

Thích hđt thì chiều :))

x² + 3x - 10

= ( x² + 3x + 9/4 ) - 49/4

= ( x + 3/2 )² - ( 7/2 )²

= ( x + 3/2 - 7/2 )( x + 3/2 + 7/2 )

= ( x - 2 )( x + 5 )

\(x^2+3x-10\)   

\(=x^2+2\cdot x\cdot\frac{3}{2}+\left(\frac{3}{2}\right)^2-10-\left(\frac{3}{2}\right)^2\)   

\(=\left(x+\frac{3}{2}\right)^2-\frac{49}{4}\)   

\(=\left(x+\frac{3}{2}\right)^2-\left(\frac{7}{2}\right)^2\)   

\(=\left(x+\frac{3}{2}-\frac{7}{2}\right)\cdot\left(x+\frac{3}{2}+\frac{7}{2}\right)\)   

\(=\left(x+5\right)\cdot\left(x-2\right)\)

Toi không thấy hđt nào ở đây cả chỉ tách thành tổng,hiệu bình phương thoi

`a^2+2sqrta+8`

`=a^2-2a+1+2a+2sqrta+7`

`=(a-1)^2+2(a+sqrta+1/4)-1/2+7`

`=(a-1)^2+(sqrta+1/2)^2+13/2`.

a: =4x^2+8x-3x-6

=4x(x+2)-3(x+2)

=(x+2)(4x-3)

b: =3(3x^2-2x-1)

=3(3x^2-3x+x-1)

=3(x-1)(3x+1)

c: =2x^2-4x+x-2

=2x(x-2)+(x-2)

=(x-2)(2x+1)

d: =3x^2+3x-2x-2

=3x(x+1)-2(x+1)

=(x+1)(3x-2)

e: =3x^2+9x+x+3

=3x(x+3)+(x+3)

=(x+3)(3x+1)

a) \(4x^2+5x-6\)

\(=4x^2+8x-3x-6\)

\(=\left(4x^2+8x\right)-\left(3x+6\right)\)

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

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

b) \(9x^2-6x-3\)

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

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

\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)

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

c) \(2x^2-3x-2\)

\(=2x^2-4x+x-2\)

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

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

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

d) \(3x^2+x-2\)

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

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

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

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

e) \(3x^2+10x+3\)

\(=3x^2+9x+x+3\)

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

\(=\left(x+3\right)\left(3x+1\right)\)

giups mình với nha

a. \(x^2-10x+25=\left(x-5\right)^2\)

b.\(4-4x^2+x^4=\left(2-x^2\right)^2\)

c. \(x^2-6y+9y^2=\left(x-3y\right)^2\)

d. \(\left(2x+y^2\right)\left(2x-y^2\right)=4x^2-y^4\)

a) x² - 10x + 25x = ( x - 5)²

b) 4 - 4x² + x⁴ = ( 2 - x² )²

c) x² - 6xy + 9y² = (x - 3y )²

d_ (2x + y² ). (2x - y² ) = 4x² - y⁴