Exercice - Factoriser, égalités remarquables

\(A = 4(x-3)^2-100\)
\(A = (2(x-3))^2 - (10)^2\)
\(A = (2x-6)^2 - (10)^2\)
\(A = (2x-6 - 10)(2x-6+10)\)
\(A = (2x-16)(2x+4)\)
\(A = 4(x-8)(x+2)\)

\(B = 49x^2-126x +81\)
\(B = (7x)^2 - 2\times7x\times 9 + (9)^2\)
\(B = (7x-9)^2\)

\(C = 0,49x^2 + 2,8x + 4\)
\(C = (0,7x)^2 + 2\times 0,7x\times 2 + 2^2\)
\(C = (0,7x+2)^2\)

\(D = (4-5x)^2-121x^2\)
\(D = (4-5x)^2-(11x)^2\)
\(D = (4-5x -11x)(4-5x+11x)\)
\(D = (-16x +4)(6x+4)\)
\(D = 8(-4x+1)(3x+2)\)

\(E =100x^2 + 80x +16 -(4x^2+4x+1)\)
\(E =(10x)^2 + 2\times 10x\times 4 +4^2 -((2x)^2+2\times 2x \times 1+1^2)\)
\(E = (10x+4)^2-(2x+1)^2\)
\(E = (10x+4+2x+1)(10x+4-2x-1)\)
\(E = (12x+5)(8x+3)\)