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(2x-9)(x+10)
(A) 2x^(2)+11 x-90
(B) 2x^(2)-9x-90
(C) 2x^(2)+9x-90
(D) 2x^(2)-11 x-90

(2x9)(x+10)(2 x-9)(x+10)\newline(A) 2x2+11x902 x^{2}+11 x-90\newline(B) 2x29x902 x^{2}-9 x-90\newline(C) 2x2+9x902 x^{2}+9 x-90\newline(D) 2x211x902 x^{2}-11 x-90

Full solution

Q. (2x9)(x+10)(2 x-9)(x+10)\newline(A) 2x2+11x902 x^{2}+11 x-90\newline(B) 2x29x902 x^{2}-9 x-90\newline(C) 2x2+9x902 x^{2}+9 x-90\newline(D) 2x211x902 x^{2}-11 x-90
  1. Identify binomials: Identify the binomials to be multiplied.\newlineWe have two binomials: (2x9)(2x-9) and (x+10)(x+10).
  2. Apply distributive property: Apply the distributive property (also known as the FOIL method) to multiply the binomials.\newlineFirst terms: 2x×x=2x22x \times x = 2x^2\newlineOuter terms: 2x×10=20x2x \times 10 = 20x\newlineInner terms: 9×x=9x-9 \times x = -9x\newlineLast terms: 9×10=90-9 \times 10 = -90
  3. Combine like terms: Combine like terms from the multiplication.\newlineCombine 20x20x and 9x-9x to get 11x11x.\newlineSo, the expression becomes 2x2+11x902x^2 + 11x - 90.