Question

Phân tích các đa thức sau thành nhân từ :

a) \(x^2+6x+9\)

b) \(10x-25-x^2\)

c) \(8x^3-\dfrac{1}{8}\)

d) \(\dfrac{1}{25}x^2-64y^2\)

Answer 1

Bài giải:

a) x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

b) 10x – 25 – x² = -(-10x + 25 +x²) = -(25 – 10x + x²)

= -(5² – 2 . 5 . x – x²) = -(5 – x)²

c) 8x³ - $\frac{1}{8}$ = (2x)³ – ($\frac{1}{2}$)³ = (2x - $\frac{1}{2}$)[(2x)² + 2x . $\frac{1}{2}$ + ($\frac{1}{2}$)²]

^{= (2x - $\frac{1}{2}$)(4x2 + x + $\frac{1}{4}$)}

d) $\frac{1}{25}$x² – 64y² = ${\left(\frac{1}{5}x\right)}^2$- (8y)² = ($\frac{1}{5}$x + 8y)($\frac{1}{5}$x - 8y)

Answer 2

a) x2 + 6x + 9 = x2 + 2.3x + 32 = (x + 3)2

b) 10x – 25 – x2 = -(x2 -10x + 25) = -(x2 -2.5x + 52)

= -(x – 5)2

c) 8x3 – 1/8= (2x)3 – ( 1/2)3 = (2x – 1/2)[(2x)2 + 2x . 1/2+ (1/2)2]

= (2x – 1/2)(4x2 + x + 1/4)

d) 1/25x2 – 64y2 = (1/5 x)2– (8y)2 = ( 1/5 x + 8y)(1/5x- 8y)