Q. Expand.Your answer should be a polynomial in standard form.(1−5z)(2−5z)=
Apply distributive property: Apply the distributive property (also known as the FOIL method) to expand the expression (1−5z)(2−5z).First, multiply the first terms in each binomial: 1×2.
Multiply first terms: Multiply the outer terms in each binomial: 1×(−5z).
Multiply outer terms: Multiply the inner terms in each binomial: (−5z)×2.
Multiply inner terms: Multiply the last terms in each binomial: (−5z)×(−5z).
Multiply last terms: Combine the results from steps 1 to 4 to get the expanded form.1×2=21×(−5z)=−5z(−5z)×2=−10z(−5z)×(−5z)=25z2Now, add all these results together: 2−5z−10z+25z2.
Combine results: Combine like terms −5z and −10z to simplify the expression.2−5z−10z+25z2=2−15z+25z2
Combine like terms:Write the polynomial in standard form, which means ordering the terms from highest degree to lowest degree.The standard form is 25z2−15z+2.