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Your answer should be a polynomial in standard form.

(3k+4)(9k+5)=

Expand.\newlineYour answer should be a polynomial in standard form.\newline(3k+4)(9k+5)=(3k+4)(9k+5)=

Full solution

Q. Expand.\newlineYour answer should be a polynomial in standard form.\newline(3k+4)(9k+5)=(3k+4)(9k+5)=
  1. Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to expand the expression (3k+4)(9k+5)(3k+4)(9k+5).\newlineFirst, multiply the first terms in each binomial: 3k×9k=27k23k \times 9k = 27k^2.
  2. Multiply first terms: Multiply the outer terms in the binomials: 3k×5=15k3k \times 5 = 15k.
  3. Multiply outer terms: Multiply the inner terms in the binomials: 4×9k=36k4 \times 9k = 36k.
  4. Multiply inner terms: Multiply the last terms in each binomial: 4×5=204 \times 5 = 20.
  5. Multiply last terms: Combine the like terms from the products obtained in steps 22 and 33.\newline15k+36k=51k15k + 36k = 51k.
  6. Combine like terms: Write the expanded form by combining all the products from steps 11, 22, 33, and 44. 27k2+51k+2027k^2 + 51k + 20.
  7. Write expanded form: Ensure that the polynomial is in standard form, which means it should be written in descending order of the powers of kk.\newlineThe terms are already in descending order: 27k227k^2 (second-degree term), 51k51k (first-degree term), and 2020 (constant term).

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