Mathematics MCQs

Distribute negative: \\(3x^2 + 2x - x^2 + 4x = 2x^2 + 6x\\).

Use identity: \\((a+b)^2 = a^2 + 2ab + b^2\\). So, \\(x^2 + 2(x)(4) + 4^2 = x^2 + 8x + 16\\).

Use identity: \\((a-b)^2 = a^2 - 2ab + b^2\\). So, \\((2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9\\).

Use identity: \\(a^2 - b^2 = (a+b)(a-b)\\). So, \\((5x)^2 - 2^2 = 25x^2 - 4\\).

Take common factor 3: \\(3(x + 2y)\\).

Find factors of 6 that add to 5: 2 and 3. So, \\((x+2)(x+3)\\).

Find factors of 12 that add to -7: -3 and -4. So, \\((x-3)(x-4)\\).

Find factors of 2×3=6 that add to 7: 1 and 6. So, \\(2x^2 + 6x + x + 3 = 2x(x+3) + 1(x+3) = (2x+1)(x+3)\\).

Expand both: \\(x^2+6x+9 - (x^2-4x+4) = x^2+6x+9 - x^2+4x-4 = 10x + 5\\).

Work inside out: \\(4x - [3y - {2x - 3x + 2y}] = 4x - [3y - {-x + 2y}] = 4x - [3y + x - 2y] = 4x - [x + y] = 4x - x - y = 3x - y\\).