The right presentation of the question is:
(a) Write 32 + 24 as a product of the two factors using the GCF and the distributive property.
(b) Write 32 + 23 as a product of the two factors using the GCF and the distributive property.
Answer:
[tex](a)\ 32 + 24 = 8*7[/tex]
[tex](b)\ 32 + 23 = 5*11[/tex]
Step-by-step explanation:
Solving (a):
First, we take the GCF of 32 and 24
[tex]32 = 2 * 2 * 2 * 2 * 2[/tex]
[tex]24 = 2 * 2 * 2 * 3[/tex]
Take common factors:
[tex]GCF = 2 * 2 * 2[/tex]
[tex]GCF = 8[/tex]
So, we factorize 32 and 24 using 8.
The expression becomes:
[tex]32 + 24 = 8(4 + 3)[/tex]
Simplify the expression in bracket
[tex]32 + 24 = 8(7)[/tex]
Remove bracket
[tex]32 + 24 = 8*7[/tex]
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Solving (b):
[tex]32 + 23 =[/tex]
32 and 23 do not have a common factor, so we have to start by writing 32 as 30 + 2
[tex]32 + 23 = 30 + 2 + 23[/tex]
Add 2 to 23
[tex]32 + 23 = 30 + 25[/tex]
Take the GCF of 30 and 25
[tex]30 = 2 * 3 * 5[/tex]
[tex]25 = 5 * 5[/tex]
Take common factors:
[tex]GCF = 5[/tex]
So, we factorize 30 and 25 using 5.
[tex]32 + 23 = 5(6 + 5)[/tex]
Simplify the expression in bracket
[tex]32 + 23 = 5(11)[/tex]
Remove bracket
[tex]32 + 23 = 5*11[/tex]
