Asked by Yuzuna Tanaka on Jun 10, 2024
Verified
Use a special product pattern to find the product [9u+(v+10) ]2[ 9 u + ( v + 10 ) ] ^ { 2 }[9u+(v+10) ]2 .
A) 81u2+v2+18uv+180u+20v+10081 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 10081u2+v2+18uv+180u+20v+100
B) 81u2+v2+20v+10081 u ^ { 2 } + v ^ { 2 } + 20 v + 10081u2+v2+20v+100
C) 81u2+v2+180u+20v+10081 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 10081u2+v2+180u+20v+100
D) 81u2+v2+10081 u ^ { 2 } + v ^ { 2 } + 10081u2+v2+100
E) 81u2+v2+18uv+20v+10081 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 10081u2+v2+18uv+20v+100
Special Product Pattern
Refers to algebraic identities that simplify the multiplication or factoring of certain algebraic expressions, such as the square of a binomial.
- Engage special product rules to aid in the simplification of polynomial-based expressions.
Verified Answer
NP
Nguy?n Ph?ng
Jun 16, 2024
Final Answer :
A
Explanation :
The correct expansion using the special product pattern (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2 for a=9ua = 9ua=9u and b=v+10b = v + 10b=v+10 gives 81u2+2(9u)(v+10)+(v+10)281u^2 + 2(9u)(v+10) + (v+10)^281u2+2(9u)(v+10)+(v+10)2 , which simplifies to 81u2+18uv+180u+v2+20v+10081u^2 + 18uv + 180u + v^2 + 20v + 10081u2+18uv+180u+v2+20v+100 .
Learning Objectives
- Engage special product rules to aid in the simplification of polynomial-based expressions.