Question

BT: Viết biểu thức sau về dạng bình phương hoặc dạng tích.
a, x⁴ - 8x² + 16
b, (4x+5)² - (5x+4)²
c, (2x-3)² - 2(2x-3).(x+2) + (-x-2)² 

Answer 1

a, \(x^4-8x^2+16=\left(x^2-4\right)^2\)

b, \(\left(4x+5\right)^2-\left(5x+4\right)^2=\left(4x+5-5x-4\right)\left(4x+5+5x+4\right)=\left(1-x\right)\left(9x+9\right)=9\left(1-x\right)\left(1+x\right)=9\left(1-x^2\right)\)

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

Answer 2

a) \(x^4-8x^2+16=\left(x^2-4\right)^2\)

b) \(\left(4x+5\right)^2-\left(5x+4\right)^2=\left(4x+5-5x-4\right)\left(4x+5+5x+4\right)=9\left(1-x\right)\left(x+1\right)\)c) \(\left(2x-3\right)^2-2.\left(2x-3\right)\left(x+2\right)+\left(-x-2\right)^2=\left(2x-3-x-2\right)^2=\left(x-5\right)^2\)