Question

Rút gọn:

a) A = ( 2x + 3 )² - 2( x + 3)( 2x + 5) + ( 2x + 5)²

b) B = ( x² + x + 1)² ( x² - x + 1 )( x² - 1)

c) C = ( 4x - 1)³ - ( 4x - 3 )( 16x² + 3)

Answer 1

a) Ta có: \(A=\left(2x+3\right)^2-2\left(x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)

\(=4x^2+12x+9-2\left(2x^2+5x+6x+15\right)+4x^2+20x+25\)

\(=8x^2+32x+34-2\left(2x^2+11x+15\right)\)

\(=8x^2+32x+34-4x^2-22x-30\)

\(=4x^2+10x-4\)

b) Sửa đề: \(B=\left(x^2+x+1\right)^2-\left(x^2-x+1\right)\left(x^2-1\right)\)

Ta có: \(B=\left(x^2+x+1\right)^2-\left(x^2-x+1\right)\left(x^2-1\right)\)

\(=x^4+x^2+1+2x^3+2x^2+2x-\left(x^4-x^2-x^3+x+x^2-1\right)\)

\(=x^4+3x^2+2x^3+2x+1-x^4+x^3-x+1\)

\(=3x^3+3x^2+x+2\)

c) Ta có: \(C=\left(4x-1\right)^3-\left(4x-3\right)\left(16x^2+3\right)\)

\(=64x^3-48x^2+12x-1-\left(64x^3+12x-48x^2-9\right)\)

\(=64x^3-48x^3+12x-1-64x^3-12x+48x^2+9\)

\(=8\)