Question

Aiza earns (3b + 1) (3b - 1) thousand pesos while Kate earns (3b + 1)² thousand pesos,
Who earns more? By how much more?
please show your solution.​

Answer 1

SOLUTION

GIVEN

Aiza earns (3b + 1) (3b - 1) thousand pesos while Kate earns (3b + 1)² thousand pesos

TO DETERMINE

Who earns more? By how much more?

EVALUATION

Here it is given that

Aiza earns (3b + 1) (3b - 1) thousand pesos while Kate earns (3b + 1)² thousand pesos

So the number of pesos earned by Aiza

$\sf{ = (3b + 1)(3b - 1)} \: \: \: \: thousand$

$\sf{ = {(3b)}^{2} - {(1)}^{2} } \: \: \: \: thousand$

$\sf{ = (9{b}^{2} - 1 )} \: \: \: \: thousand$

Again the number of pesos earned by Kate

$\sf{ = {(3b + 1)}^{2} \: \: \: \: thousand}$

$\sf{ = {(3b )}^{2} + 2 \times 3b \times 1 + {(1)}^{2} \: \: \: \: thousand}$

$\sf{ =(9 {b }^{2} + 6b + 1 ) \: \: \: \: thousand}$

So Kate earned more pesos than Aiza

The number of pesos Kate earned more than Aiza

$\sf{ =(9 {b }^{2} + 6b + 1 ) \: \: \: \: thousand }- \sf{ (9 {b }^{2} - 1 ) \: \: \: \: thousand}$

$\sf{ =(6b + 2) \: \: \: \: thousand}$

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