Question

[Nguyễn Hoàng Gia Hân]

Chứng minh đẳng thức sau:

a) (a + b + c) . (a - b + c) = a² - b² + c² + 2ac

b) (3x + 2y) . (3x - 2y) - (4x - 2y) . (4x + 2y) = -7x²

c) (x - 1) . (x² + x + 1) - (x +1) . (x² - x +1) = -2

d) (2x + 1) . (4x² - 2x + 1) - (2x - 1) . (4x² +2x + 1) = 2

e) (x - 2y) . (x² + 2xy + 4y²) - (2x - 1) . (x² + 2xy + 4y²) = -16y³

Answer 1

[lê thị hương giang]

\(a,VT=\left(a+b+c\right)\left(a-b+c\right)\)

\(=\left(a+c+b\right)\left(a+c-b\right)\)

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

\(=a^2+2ac+c^2-b^2=VP\)

\(b,VT=\left(3x+2y\right)\left(3x-2y\right)-\left(4x-2y\right)\left(4x+2y\right)\)

\(=9x^2-4y^2-16x^2+4y^2=-7x^2=VP\)

\(c,VT=x^3-1-x^3-1=-2=VP\)

\(d,VT=8x^3+1-8x^3+1=2=VP\)

\(e,VT=\left(x^2+2xy+4y^2\right)\left(x-2y-2x+1\right)\)

\(=\left(x^2+2xy+4y^2\right)\left(-x-2y+1\right)\)

\(=-x^3-2x^2y+x^2-2x^2y-4xy^2+2xy-4xy^2-8y^3+4y^2\)

( bn kiểm tra lại đề nhé)