Question - Algebraic Expansion of Polynomial Expressions

Câu 2:

\[(x+1)(x+2)(x+3)(x+4) - 24\]

\[= [(x^2+3x+2)(x^2+7x+12)] - 24\]

\[= [x^4+7x^3+12x^2+3x^3+21x^2+6x+2x^2+14x+24] - 24\]

\[= x^4+10x^3+35x^2+20x\]

Câu 4:

\[x^4 + x^2 + 4x^2 + 4x -12\]

\[= x^4 + 5x^2 + 4x - 12\]

Câu 6:

\[(x+a)(x+2a)(x+3a)(x+4a) + a^4\]

\[= [(x^2+5ax+4a^2)(x^2+5ax+6a^2)] + a^4\]

\[= [x^4+5ax^3+6a^2x^2+5ax^3+25a^2x^2+30a^3x+4a^2x^2+20a^3x+24a^4] + a^4\]

\[= x^4+10ax^3+35a^2x^2+50a^3x+25a^4\]

Câu 8:

\[(x^4 + x^2)^2 + 3(x^2 + x) + 2\]

\[= x^8 + 2x^6 + x^4 + 3x^2 + 3x + 2\]

Câu 10:

\[(x^4 + 2x^2)^2 + 9x^2 + 18x + 20\]

\[= x^8 + 4x^6 + 4x^4 + 9x^2 + 18x + 20\]

Câu 12:

\[(x^2 + 2)(x^4 + 4)(x^6 + 6)(x^8 + 8) + 16\]

\[= (x^12 + 2x^10 + 4x^8 + 8x^6 + 6x^4 + 12x^2 + 8) + 16\]

\[= x^12 + 2x^10 + 4x^8 + 8x^6 + 6x^4 + 12x^2 + 24\]