Question

Phân tích đa thức thành nhân tử:

1) x²-14x+49-4a²

2) 9x²+6x+1-25

 

Answer 1

1) 

\(=\left(x-7\right)^2-4a^2\)

\(=\left(x-7+2a\right)\left(x-7-2a\right)\)

2)

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

\(=\left(3x+1+5\right)\left(3x+1-5\right)\)

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

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

Answer 2

1)x^2-14x+49-4a^2

=x^2-2x7+7^2-4a^2

=\(\left(x-7\right)^2-4a^2\)

=\(\left(x-7\right)^2-\left(2a\right)^2\)

=\(\left(\left(x-7\right)-\left(2a\right)\right).\left(\left(x-7\right)+\left(2a\right)\right)\)

=\(\left(x-7-2a\right).\left(x-7+2a\right)\)

b)

\(9x^2+6x+1-25\\ =\left(3x\right)^2-5^2+6x+1\\ =\left(\left(3x\right)-5\right).\left(\left(3x\right)+5\right)+6x+1\)

\(=\left(3x-5\right).\left(3x+5\right)+6x+1\)

Answer 3

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 - 1/8 = (2x)³ – (1/2)³ = (2x - 1/2)[(2x)² + 2x . 12 + (1/2)²]

                    ^{= (2x - 1/2)(4x2 + x + 1/4)} 

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