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Expand.
Your answer should be a polynomial in standard form.

(1-5z)(2-5z)=

Expand.\newlineYour answer should be a polynomial in standard form.\newline(15z)(25z)=(1-5z)(2-5z)=

Full solution

Q. Expand.\newlineYour answer should be a polynomial in standard form.\newline(15z)(25z)=(1-5z)(2-5z)=
  1. Apply distributive property: Apply the distributive property (also known as the FOIL method) to expand the expression (15z)(25z)(1-5z)(2-5z).\newlineFirst, multiply the first terms in each binomial: 1×21 \times 2.
  2. Multiply first terms: Multiply the outer terms in each binomial: 1×(5z)1 \times (-5z).
  3. Multiply outer terms: Multiply the inner terms in each binomial: (5z)×2(-5z) \times 2.
  4. Multiply inner terms: Multiply the last terms in each binomial: (5z)×(5z)(-5z) \times (-5z).
  5. Multiply last terms: Combine the results from steps 11 to 44 to get the expanded form.\newline1×2=21 \times 2 = 2\newline1×(5z)=5z1 \times (-5z) = -5z\newline(5z)×2=10z(-5z) \times 2 = -10z\newline(5z)×(5z)=25z2(-5z) \times (-5z) = 25z^2\newlineNow, add all these results together: 25z10z+25z22 - 5z - 10z + 25z^2.
  6. Combine results: Combine like terms 5z-5z and 10z-10z to simplify the expression.25z10z+25z2=215z+25z22 - 5z - 10z + 25z^2 = 2 - 15z + 25z^2
  7. Combine like terms: Write the polynomial in standard form, which means ordering the terms from highest degree to lowest degree.\newlineThe standard form is 25z215z+225z^2 - 15z + 2.

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