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Sagot :
SIMPLIFYING
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5.) Simplify (x2n + 2y)2 (x3n)0
[tex]\rm{Interpreted \ Question: \underline{(x^{2} n + 2y)^{2} (x^{3n} )^{0} }}[/tex]
Any number raised to the power of 0 equals to 1. Hence, (x^{3n})⁰ = 1.
- [tex]= (x^{2} n + 2y)^{2} (x^{3n} )^{0}[/tex]
- [tex]= (x^{2} n + 2y)^{2} \times 1[/tex]
- [tex]= \underline{\green{(x^{2} n + 2y)^{2}}}[/tex]
Hence, the simplified form is (x²n + 2y)²
[tex]\\[/tex]
6.) Simplify x2y(2x3 + 3x2y - 3xy2 + 2y3)
Distribute x²y to all terms in the parentheses
- [tex]x^{2} y(2x^{3} + 3x^{2} y - 3xy^{2} + 2y^{3} )[/tex]
- [tex]{=x^{2} y \times 2x^{3} + x^{2} y \times 3x^{2} y - x^{2} y \times 3xy^{2} + x^{2} y \times 2y^{3} }[/tex]
- [tex]{=2x^{3+2}y + 3x^{2+2}y^{2} - 3x^{2+1}y^{1+2} + 2x^{2} y^{1+3} }[/tex]
- [tex]\underline{\green{=2x^{5}y + 3x^{4}y^{2} - 3x^{3}y^{3}+ 2x^{2}y^{4} }}[/tex]
Hence, the simplified form is [tex]{2x^{5}y + 3x^{4}y^{2} - 3x^{3}y^{3}+ 2x^{2}y^{4} }[/tex].
[tex]\\[/tex]
7.) Factor (x2 - 34x – 72) by grouping.
To begin factoring this, we first need to find two numbers that multiply to -72 and numbers that add to -34. These numbers would be -36 and 2. (-36 × 2 = -72, -36 + 2 = -34.) Rewrite the expression using -36x and 2x.
- [tex]= (x^{2} - 34x - 72)[/tex]
- [tex]= x^{2} - 36x + 2x - 72[/tex]
- [tex]= (x^{2} - 36x) + (2x - 72)[/tex]
- [tex]= x(x-36) + 2(x - 36)[/tex]
- [tex]\underline{\green{= (x-36) (x +2)}}[/tex]
Hence, the factored form is (x - 36)(x + 2)
[tex]\\[/tex]
8.) Simplify the product of(x - y)(x2 + xy + y2)
- [tex]= (x-y)(x^{2} +xy+y^{2} )[/tex]
- [tex]{= x(x^{2} +xy+y^{2} ) - y(x^{2} +xy+y^{2} )}[/tex]
- [tex]{= x^{3} +x^{2} y+xy^{2} - yx^{2} -y^{2} x-y^{3}}[/tex]
- [tex]{= x^{3} +x^{2} y+xy^{2} - x^{2}y -xy^{2}-y^{3}}[/tex]
- [tex]\underline{\green{= x^{3} -y^{3}}}[/tex]
Hence, the factored form is x³-y³.
[tex]\\[/tex]
9.) Simplify the product of (x2 - 2y)(x3 + 3y2)
- [tex]= (x^{2} - 2y)(x3 + 3y^{2} )[/tex]
- [tex]{= x^{2}(x^{3} + 3y^{2} ) - 2y(x^{3} + 3y^{2} )}[/tex]
- [tex]{= x^{2} \times x^{3} + x^{2} \times 3y^{2} - 2y \times x^{3} - 2y \times 3y^{2}}[/tex]
- [tex]\underline{\green{= x^{5}+3x^{2} y^{2} - 2x^{3}y - 6y^{3}}}[/tex]
Hence, the simplified form is [tex]{x^{5}+3x^{2} y^{2} - 2x^{3}y - 6y^{3}}[/tex].
[tex]\\[/tex]
10.) Factor (5x – 2y)2 - (x + 3y)2
Using the formula (a²-b²) = (a-b)(a+b), where a = (5x-2y), and b = (x+3y).
- [tex]= (5x - 2y)^{2} - (x + 3y)^{2}[/tex]
- [tex]{= [(5x - 2y) - (x + 3y)] [(5x - 2y) - (x + 3y)]}[/tex]
- [tex]{= (5x - 2y - x - 3y)(5x - 2y+x + 3y)}[/tex]
- [tex]\underline{\green{{= (4x - 5y)(6x +y)}}}[/tex]
Hence, the factored form is (4x-5y)(6x+y).
[tex]\normalsize{\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}}}[/tex]
[tex]\sf{Swipe \: right \rightarrow \: if \: you \: are \: using \: the\: brainly \: app}[/tex]
[tex]\large{\boxed{\tt{\blue{06/09/2024}}}}[/tex]
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