which expression is equivalent to ( n^{2}+26n + 88 ) for all values of ( n )?\n( (n + 8)(n + 11) )\n( (n +…

which expression is equivalent to ( n^{2}+26n + 88 ) for all values of ( n )?\n( (n + 8)(n + 11) )\n( (n + 4)(n + 22) )\n( (n + 4)(n + 24) )\n( (n + 8)(n + 18) )

which expression is equivalent to ( n^{2}+26n + 88 ) for all values of ( n )?\n( (n + 8)(n + 11) )\n( (n + 4)(n + 22) )\n( (n + 4)(n + 24) )\n( (n + 8)(n + 18) )

Answer

Explanation:

Step1: Expand ((n + a)(n + b)=n^{2}+(a + b)n+ab)

We need to find (a) and (b) such that (a + b=26) and (ab = 88).

Step2: Check each option

  • For ((n + 8)(n + 11)): (a=8), (b = 11), (a + b=8+11=19\neq26), (ab=8\times11 = 88)
  • For ((n + 4)(n + 22)): (a = 4), (b=22), (a + b=4+22=26), (ab=4\times22=88)
  • For ((n + 4)(n + 24)): (a = 4), (b=24), (a + b=4 + 24=28\neq26), (ab=4\times24=96\neq88)
  • For ((n + 8)(n + 18)): (a=8), (b = 18), (a + b=8+18=26), (ab=8\times18=144\neq88)

Answer:

((n + 4)(n + 22))