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Write the expression in simplest form. 2r[1-3s-2(r-s-1)-r]

Write the expression in simplest form.\newline2r[1−3s−2(r−s−1)−r] 2 r[1-3 s-2(r-s-1)-r]

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Full solution

Q. Write the expression in simplest form.\newline2r[1−3s−2(r−s−1)−r] 2 r[1-3 s-2(r-s-1)-r]
  1. Distribute 2r2r: First, distribute the 2r2r inside the brackets.\newline2r×1=2r2r \times 1 = 2r\newline2r×(−3s)=−6rs2r \times (-3s) = -6rs\newline2r×−2(r−s−1)=−4r(r−s−1)2r \times -2(r - s - 1) = -4r(r - s - 1)\newline2r×−r=−2r22r \times -r = -2r^2
  2. Distribute −4r-4r: Now, distribute the −4r-4r inside the parentheses.\newline−4r×r=−4r2-4r \times r = -4r^2\newline−4r×−s=+4rs-4r \times -s = +4rs\newline−4r×−1=+4r-4r \times -1 = +4r
  3. Combine terms: Combine all the terms we've got.\newline2r−6rs−4r2+4rs+4r−2r22r - 6rs - 4r^2 + 4rs + 4r - 2r^2
  4. Simplify terms: Now, let's simplify by combining like terms.\newline2r+4r=6r2r + 4r = 6r\newline−6rs+4rs=−2rs-6rs + 4rs = -2rs\newline−4r2−2r2=−6r2-4r^2 - 2r^2 = -6r^2
  5. Final expression: So, the simplified expression is: 6r−2rs−6r26r - 2rs - 6r^2

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