Answers:
5) product is [tex]35ax^2 - 42axy + 7y^2[/tex]
6) product is [tex]-a^6b^2 - 8a^5b - 5a^4[/tex]
7) product is [tex]12x^5y + 6x^4y^2 + 21x^3y^3[/tex]
8) product is [tex]3x^3y^2 - 6x^3y + 3x^5y - 3x^4y[/tex]
9) product is [tex]x^{3n} + 7x^{n+1} - 3x^n[/tex]
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Explanation:
For each of these questions, you'll multiply the term outside by each term inside the parenthesis. I'm using the distributive property.
In problem 5, we multiply the outer 7a by the following terms inside like so
[tex]7a(5x^2-2xy+y^2-4xy)\\\\7a(5x^2-6xy+y^2)\\\\7a(5x^2)+7a(-6xy)+7a(y^2)\\\\35ax^2-42axy+7ay^2\\\\[/tex]
The other problems will have similar steps.
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A useful rule to keep in mind is that [tex]a^b*a^c = a^{b+c}[/tex]
For example, [tex]x^2*x^3 = x^{2+3} = x^5[/tex]