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Common Core Standard HSA-APR.C.5 Questions

(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1

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Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Expand the binomial (x-3)4 using Pascal's Triangle.
  1. x4+12x3+54x2+108x+81
  2. x4-12x3+54x2-108x+81
  3. x4-12x3-54x2-108x-81
  4. x4-12x3+18x2-36x+81
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 3rd term in expansion (2x-3)5.
  1. 720x3
  2. 80x3
  3. 72x3
  4. 120x3
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Find the 7th term in expansion (x+y)8.
  1. 8x2y6
  2. 28x2y6
  3. 70x2y6
  4. 56x2y6
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
How can one determine the coefficients of the Binomial Theorem expansion for (x+y)n, where n is an integer? There may be more than one correct answer.
  1. Pascal's Triangle
  2. Binomial Permutation
  3. (nk), k=0,...,n
  4. n!k!(n-k)!, k=0,...,n
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Use Pascal's triangle to expand (x+y)3.
  1. (x+y)3=x3+y3
  2. (x+y)3=x1+x2+x3+y1+y2+y3
  3. (x+y)3=x3+3x2y+3xy2+y3
  4. (x+y)3=xy+3x2y2+9x3y3
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.5
Use Pascal's triangle to expand (x+y)5.
  1. (x+y)5=x5+5x4y+10x3y2+10x2y3+4xy4+y5
  2. (x+y)5=x1+x2+x3+x4+x5+y1+y2+y3+y4+y5
  3. (x+y)5=x5+y5
  4. (x+y)5=xy+5x2y2+10x3y3+15x4y4+20x5y5

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