Answer:
1. 90
2. 45
3. 75
4. 45
5. 135
6. 105
7. 180
8. 150
9. 180
10. 210
Step-by-step explanation:
POLYNOMIAL
Multiplying Polynomials
1.
MATHEMATICAL PROBLEM
(x^{2} -6x+9)(x+2)(x
2
−6x+9)(x+2)
SOLUTION
\begin{gathered}(x^{2} -6x+9)(x+2)\\\\=x^2x+x^2\cdot \:2+\left(-6x\right)x+\left(-6x\right)\cdot \:2+9x+9\cdot \:2\\\\=x^2x+2x^2-6xx-6\cdot \:2x+9x+9\cdot \:2\\\\=x^3-4x^2-3x+18\end{gathered}
(x
=x
x+x
⋅2+(−6x)x+(−6x)⋅2+9x+9⋅2
x+2x
−6xx−6⋅2x+9x+9⋅2
3
−4x
−3x+18
ANSWER
=x^3-4x^2-3x+18=x
2.
(2m^{2} n + 3mn + n^{2} ) - 3m^{2} n - mn - 2n^{2} )(2m
n+3mn+n
)−3m
n−mn−2n
)
\left(2m^2n+3mn+n^2\right)(-3m^2n-mn-2n^2)(2m
)(−3m
\begin{gathered}=2m^2n+3mn+n^2-3m^2n-mn-2n^2\\\\=n^2-2n^2+2m^2n-3m^2n+3mn-mn\\\\=n^2-2n^2-m^2n+3mn-mn\\\\=n^2-2n^2-m^2n+2mn\\\\=-n^2-m^2n+2mn\end{gathered}
=2m
−3m
=n
−2n
+2m
n−3m
n+3mn−mn
−m
n+2mn
=−n
=-n^2-m^2n+2mn=−n
3.
(4x + 2xy - y) + 2x - 1)(4x+2xy−y)+2x−1)
\begin{gathered}=4x+2xy-y+2x-1\\\\=2xy+4x+2x-y-1\\\\=2xy+6x-y-1\end{gathered}
=4x+2xy−y+2x−1
=2xy+4x+2x−y−1
=2xy+6x−y−1
=2xy+6x-y-1=2xy+6x−y−1
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Answers & Comments
Answer:
1. 90
2. 45
3. 75
4. 45
5. 135
6. 105
7. 180
8. 150
9. 180
10. 210
Step-by-step explanation:
Answer:
POLYNOMIAL
Multiplying Polynomials
1.
MATHEMATICAL PROBLEM
(x^{2} -6x+9)(x+2)(x
2
−6x+9)(x+2)
SOLUTION
\begin{gathered}(x^{2} -6x+9)(x+2)\\\\=x^2x+x^2\cdot \:2+\left(-6x\right)x+\left(-6x\right)\cdot \:2+9x+9\cdot \:2\\\\=x^2x+2x^2-6xx-6\cdot \:2x+9x+9\cdot \:2\\\\=x^3-4x^2-3x+18\end{gathered}
(x
2
−6x+9)(x+2)
=x
2
x+x
2
⋅2+(−6x)x+(−6x)⋅2+9x+9⋅2
=x
2
x+2x
2
−6xx−6⋅2x+9x+9⋅2
=x
3
−4x
2
−3x+18
ANSWER
=x^3-4x^2-3x+18=x
3
−4x
2
−3x+18
2.
MATHEMATICAL PROBLEM
(2m^{2} n + 3mn + n^{2} ) - 3m^{2} n - mn - 2n^{2} )(2m
2
n+3mn+n
2
)−3m
2
n−mn−2n
2
)
SOLUTION
\left(2m^2n+3mn+n^2\right)(-3m^2n-mn-2n^2)(2m
2
n+3mn+n
2
)(−3m
2
n−mn−2n
2
)
\begin{gathered}=2m^2n+3mn+n^2-3m^2n-mn-2n^2\\\\=n^2-2n^2+2m^2n-3m^2n+3mn-mn\\\\=n^2-2n^2-m^2n+3mn-mn\\\\=n^2-2n^2-m^2n+2mn\\\\=-n^2-m^2n+2mn\end{gathered}
=2m
2
n+3mn+n
2
−3m
2
n−mn−2n
2
=n
2
−2n
2
+2m
2
n−3m
2
n+3mn−mn
=n
2
−2n
2
−m
2
n+3mn−mn
=n
2
−2n
2
−m
2
n+2mn
=−n
2
−m
2
n+2mn
ANSWER
=-n^2-m^2n+2mn=−n
2
−m
2
n+2mn
3.
MATHEMATICAL PROBLEM
(4x + 2xy - y) + 2x - 1)(4x+2xy−y)+2x−1)
SOLUTION
(4x + 2xy - y) + 2x - 1)(4x+2xy−y)+2x−1)
\begin{gathered}=4x+2xy-y+2x-1\\\\=2xy+4x+2x-y-1\\\\=2xy+6x-y-1\end{gathered}
=4x+2xy−y+2x−1
=2xy+4x+2x−y−1
=2xy+6x−y−1
ANSWER
=2xy+6x-y-1=2xy+6x−y−1