Answer:
5. (996)^2
= (1000- 4)^2
= 1000^2 + 4^2 -2(1000)(4)
= 1000000 + 16 - 8000
= 992000 + 16
= 992016.
6. [tex](105)^{2}[/tex] = [tex](100+5)^{2}[/tex] [tex][ (a+b)^{2}[/tex] [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -[tex]2ab ][/tex]
= [tex](100)^{2}[/tex] + [tex](5)^{2}[/tex] + [tex]2(5)(100)[/tex]
= 10000 + 25 + 1000
= 11025.
7. [tex](1000)^{2}[/tex] = [tex](1000 + 3)^{2}[/tex]
Suitable identities is [tex](x+y)^{2}[/tex] = [tex]x^{2}[/tex] + [tex]2x^{2} y[/tex] + [tex]2xy^{2}[/tex] + [tex]y^{2}[/tex]
∴ [tex](1000 + 3)^{2}[/tex]
= [tex](1000)^{2}[/tex] + [tex]2(1000)^{2} (3) + 2(1000)(3)^{2} + (3)^{2}[/tex]
= 1000000000 + 2000000 + 2000 + 3 = 1002002003
Step-by-step explanation:
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Answers & Comments
Answer:
5. (996)^2
= (1000- 4)^2
= 1000^2 + 4^2 -2(1000)(4)
= 1000000 + 16 - 8000
= 992000 + 16
= 992016.
6. [tex](105)^{2}[/tex] = [tex](100+5)^{2}[/tex] [tex][ (a+b)^{2}[/tex] [tex]a^{2}[/tex] + [tex]b^{2}[/tex] -[tex]2ab ][/tex]
= [tex](100)^{2}[/tex] + [tex](5)^{2}[/tex] + [tex]2(5)(100)[/tex]
= 10000 + 25 + 1000
= 11025.
7. [tex](1000)^{2}[/tex] = [tex](1000 + 3)^{2}[/tex]
Suitable identities is [tex](x+y)^{2}[/tex] = [tex]x^{2}[/tex] + [tex]2x^{2} y[/tex] + [tex]2xy^{2}[/tex] + [tex]y^{2}[/tex]
∴ [tex](1000 + 3)^{2}[/tex]
= [tex](1000)^{2}[/tex] + [tex]2(1000)^{2} (3) + 2(1000)(3)^{2} + (3)^{2}[/tex]
= 1000000000 + 2000000 + 2000 + 3 = 1002002003
Step-by-step explanation:
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