Express as a polynomial. (t^{2} + 2t - 5)(3t^{2} -

David Troyer 2021-12-17 Answered
Express as a polynomial. (t2+2t5)(3t2t+2)
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Expert Answer

Alex Sheppard
Answered 2021-12-18 Author has 36 answers
Step 1
Given:
(t2+2t5)(3t2t+2)
For the polynomial, we solve the parenthesis,
t2(3t2t+2)+2t(3t2t+2)5(3t2t+2)
3t4t3+2t2+6t32t2+4t15t2+5t10
3t45t315t2+9t10
Step 2
Hence,
The polynomial is,
3t45t315t2+9t10
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Bertha Jordan
Answered 2021-12-19 Author has 37 answers
Consider (t2+2t5)(3t2t+2)
Treating the polynomial (3t2t+2) as a single real term, and then multiplying, we get
(t2+2t5)(3t2t+2)
=(t2+2t+(5))(3t2+(t)+2)
=t2(3t2+(t)+2)+2t(3t2+(t)+2)+(5)(3t2+(t)+2)
[using distributive property]
Again, using distributive property three times, and simplifying the result, we get
=3t4t3+2t2+6t32t2+4t15t2+5t10
[adding the powers of same base]
=3t4+(1+6)t3+(2215)t2+(4+5)t10
[adding the coefficient of like powers of x]
=3t4+5t315t2+9t10 [simplifying]
The three monomials in the first polynomial were multiplied by each of the three monomials in the second polynomial, giving us a total of nine terms, whose sum is the required polynomial, is
3t4+5t315t2+9t10
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