Question

viết mỗi biểu thức sau dưới dạng hiệu hai bình phương

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

b) (x+y-1)(x+y+1)

c) (x+5)(x-5)

d) (x-y-1)(x+y+1)

Answer 1

a. 9 - x²

b. (x+y)² - 1

c.x⁵ - 25

d. x² - (y+1)²

Answer 2

a) (3 - x) . (3 + x) = 3² - x²

b) (x + y - 1) . (x + y + 1) = (x + y)² - 1²

c) (x + 5) . (x - 5) = x² - 5²

d) (x - y - 1) . (x + y + 1) = x² - (y + 1)²

Answer 3

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

b, \(\left(x+y-1\right)\left(x+y+1\right)=x^2+xy+x+xy+y^2+y-x-y-1\)

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

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

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

d, \(\left(x-y-1\right)\left(x+y+1\right)=x^2+xy+x-xy-y^2-y-x-y-1\)

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

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