Answer:
Part 1 is explained in 1) of the explanation.
Part 2 is explained in 2) of the explanation.
Step-by-step explanation:
1) So you choose 45 and to write it as 50-5.
We want to square 45 without using a calculator.
That is we want to find [tex]45^2[/tex] without a calculator.
[tex]45^2=(50-5)^2[/tex]
[tex]45^2=(50)^2-2(50)(5)+(5)^2[/tex] by your identity [tex](x-y)^2=x^2-2xy+y^2[/tex].
[tex]45^2=50(50)-100(5)+25[/tex]
[tex]45^2=2500-500+25[/tex]
[tex]45^2=2000+25[/tex]
[tex]45^2=2025[/tex]
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2) Choose two numbers for [tex]a[/tex] and [tex]b[/tex] between 8 and 15. I will choose 10 [tex](a=10)[/tex] and 12 [tex](b=12)[/tex].
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]10^3+12^3=(10+12)(10^2-10(12)+(12)^2[/tex]
[tex]10^3+12^3=(22)(100-120+144)[/tex]
[tex]10^3+12^3=(22)(-20+144)[/tex]
[tex]10^3+12^3=22(124)[/tex]
Now we have to multiply 22 and 124 without a calculator...
22(124)
(20+2)(124)
124(20)+124(2)
124(10+10)+124(2)
1240+1240+248
2480+248
2728
The required solution of Part A is 2025 and Part B is 1710.
The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.
Part A:
Let the assumed number be 45
Difference of two numbers i.e. 50 - 5 = 45
Now applying identity (x-y)² = (50 - 5)²
(50 - 5)² = 50² + 5² - 2 * 50 * 5
= 2500 + 25 - 500
= 2025
Part 2
The assumed two number is a = 9 and b = 10
10³ - 9³ = (10 + 9)(10² - 9 * 10 + 9²)
= (19)(100 - 90 + 81)
= 19 * 91
= (20 - 1)(90)
= 1800 - 90
= 1710
Thus the required solution of Part A is 2025 and Part B is 1710.
Learn more about simplification here: https://brainly.com/question/12501526
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