p.t 3a+2/4×3a-3a+1/3a=2 ( exponents)
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Answers
Answer:
(3a+1)(3a−2)(3a+4)
\mathrm{Expand}\:(3a+1)(3a-2)Expand(3a+1)(3a−2)
(3a+1)(3a-2)(3a+1)(3a−2)
\mathrm{Apply\:FOIL\:method}:\quad (a+b)(c+d)=ac+ad+bc+bdApplyFOILmethod:(a+b)(c+d)=ac+ad+bc+bd
a=3a,\:b=1,\:c=3a,\:d=-2a=3a,b=1,c=3a,d=−2
=3a\cdot \:3a+3a(-2)+1\cdot \:3a+1\cdot (-2)=3a⋅3a+3a(−2)+1⋅3a+1⋅(−2)
\mathrm{Apply\:minus-plus\:rules}Applyminus−plusrules
+(-a)=-a+(−a)=−a
=3\cdot \:3aa-3\cdot \:2a+1\cdot \:3a-1\cdot \:2=3⋅3aa−3⋅2a+1⋅3a−1⋅2
\mathrm{Simplify}\:3\cdot \:3aa-3\cdot \:2a+1\cdot \:3a-1\cdot \:2Simplify3⋅3aa−3⋅2a+1⋅3a−1⋅2
3\cdot \:3aa-3\cdot \:2a+1\cdot \:3a-1\cdot \:23⋅3aa−3⋅2a+1⋅3a−1⋅2
3\cdot \:3aa3⋅3aa
\mathrm{Multiply\:the\:numbers:}\:3\cdot \:3=9Multiplythenumbers:3⋅3=9
=9aa=9aa
\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}Applyexponentrule:a
b
⋅a
c
=a
b+c
aa=\:a^{1+1}aa=a
1+1
=9a^{1+1}=9a
1+1
\mathrm{Add\:the\:numbers:}\:1+1=2Addthenumbers:1+1=2
=9a^2=9a
2
3\cdot \:2a=6a3⋅2a=6a
1\cdot \:3a=3a1⋅3a=3a
1\cdot \:2=21⋅2=2
=9a^2-6a+3a-2=9a
2
−6a+3a−2
=(9a^2-3a-2)(3a+4)=(9a
2
−3a−2)(3a+4)
\mathrm{Expand}\:(9a^2-3a-2)(3a+4)Expand(9a
2
−3a−2)(3a+4)
(9a^2-3a-2)(3a+4)(9a
2
−3a−2)(3a+4)
\mathrm{Distribute\:parentheses}Distributeparentheses
=9a^2\cdot \:3a+9a^2\cdot \:4+(-3a)\cdot \:3a+(-3a)\cdot \:4+(-2)\cdot \:3a+(-2)\cdot \:4=9a
2
⋅3a+9a
2
⋅4+(−3a)⋅3a+(−3a)⋅4+(−2)⋅3a+(−2)⋅4
\mathrm{Apply\:minus-plus\:rules}Applyminus−plusrules
+(-a)=-a+(−a)=−a
=9\cdot \:3a^2a+9\cdot \:4a^2-3\cdot \:3aa-3\cdot \:4a-2\cdot \:3a-2\cdot \:4=9⋅3a
2
a+9⋅4a
2
−3⋅3aa−3⋅4a−2⋅3a−2⋅4
\mathrm{Simplify}\:9\cdot \:3a^2a+9\cdot \:4a^2-3\cdot \:3aa-3\cdot \:4a-2\cdot \:3a-2\cdot \:4Simplify9⋅3a
2
a+9⋅4a
2
−3⋅3aa−3⋅4a−2⋅3a−2⋅4
9\cdot \:3a^2a+9\cdot \:4a^2-3\cdot \:3aa-3\cdot \:4a-2\cdot \:3a-2\cdot \:49⋅3a
2
a+9⋅4a
2
−3⋅3aa−3⋅4a−2⋅3a−2⋅4
9\cdot \:3a^2a9⋅3a
2
a
\mathrm{Multiply\:the\:numbers:}\:9\cdot \:3=27Multiplythenumbers:9⋅3=27
=27a^2a=27a
2
a
\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}Applyexponentrule:a
b
⋅a
c
=a
b+c
a^2a=\:a^{2+1}a
2
a=a
2+1
=27a^{2+1}=27a
2+1
\mathrm{Add\:the\:numbers:}\:2+1=3Addthenumbers:2+1=3
=27a^3=27a
3
9\cdot \:4a^2=36a^29⋅4a
2
=36a
2
3\cdot \:3aa=9a^23⋅3aa=9a
2
3\cdot \:4a=12a3⋅4a=12a
2\cdot \:3a=6a2⋅3a=6a
2\cdot \:4=82⋅4=8
=27a^3+36a^2-9a^2-12a-6a-8=27a
3
+36a
2
−9a
2
−12a−6a−8
\mathrm{Add\:similar\:elements:}\:-12a-6a=-18aAddsimilarelements:−12a−6a=−18a
=27a^3+36a^2-9a^2-18a-8=27a
3
+36a
2
−9a
2
−18a−8
\mathrm{Add\:similar\:elements:}\:36a^2-9a^2=27a^2Addsimilarelements:36a
2
−9a
2
=27a
2
=27a^3+27a^2-18a-8=27a
3
+27a
2
−18a−8