a² - 6a + 9 = (a-3)²

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1-4x+4x² = (1-2x)²

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(a+b)² - 1 = (a+b-1)(a+b+1)

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4x²- 9 = (2x-3)(2x+3)

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25x² - 20xy + 4y² = (5x - 2y)²

\(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\times\left(2x+3\right)\)

\(25x^2-20xy+4y^2=\left(5x\right)^2-2\times5x\times2y+\left(2y\right)^2=\left(5x-2y\right)^2\)

a. x² + 6x + 9 = (x + 3)²

b. 25 + 10x + x² = (5 + x)²

c. x² + 8x + 16 = (x + 4)²

d. x² + 14x + 49 = (x + 7)²

e. 4x² + 12x + 9 = (2x + 3)²

f. 9x² + 12x + 4 = (3x + 2)²

h. 16x² + 8 + 1 = (4x + 1)²

i. 4x² + 12xy + 9y² = (2x + 3y)²

k. 25x² + 20xy + 4y² = (5x + 2y)²

a) \(=\left(x+3\right)^2\)

b) \(=\left(x+5\right)^2\)

c) \(=\left(x+4\right)^2\)

d) \(=\left(x+7\right)^2\)

e) \(=\left(2x+3\right)^2\)

f) \(=\left(3x+2\right)^2\)

h) \(=\left(4x+1\right)^2\)

i) \(=\left(2x+3y\right)^2\)

k) \(=\left(5x+2y\right)^2\)

a,9a²-30a+25

=(3a)²-30a+5²

=(3a-5)²

b,1+4x+4x²

=4x²+4x+1

=(2x)²+4x+1²

=(2x+1)²

c,a²+16+8a

=a²+8a+16

=a²+8a+4²

=(a+2)²

d,25x²+4y²-20xy

=25x²-20xy+4y²

=(5x)²-20xy+(2y)²

=(5x-2y)²

a) \(25x^2-20xy+4y^2\)

\(=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\)

\(=\left(5x-2y\right)^2\)

b) \(4x^2+9+12x\)

\(=\left(2x\right)^2+3^2+2.2x.3\)

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

c) \(\frac{1}{4}+3x+9x^2\)

\(=\left(\frac{1}{2}\right)^2+2.\frac{1}{2}.3x+\left(3x\right)^2\)

\(=\left(\frac{1}{2}+3x\right)^2\)

d) \(-6xy+x^2+9y^2\)

\(=x^2-6xy+9y^2\)

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

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

Nguyễn Bích Quỳnh: bạn chúc như một vị thần

a) \(x^2+x+\frac{1}{4}=\left(x+\frac{1}{2}\right)^2\)

b) \(x^2+12xy+36y^2=\left(x+6y\right)^2\)

c) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

d) Không phải hằng đẳng thức \(\left(x^2-2x+4=\left(x-1\right)^2+3\right)\)

e) \(25x^2+4y^2-20xy=\left(5x-2y\right)^2\)

b: \(\left(a-b\right)^2-c^2=\left(a-b-c\right)\left(a-b+c\right)\)

c: \(4x^2+12x+9=\left(2x+3\right)^2\)

d: \(25x^2-20xy+4y^2=\left(5x-2y\right)^2\)

e: \(8x^6-27y^3=\left(2x^2-3y\right)\left(4x^2+6x^2y+9y^2\right)\)