(97xy) ³ answer it like 5 mark Q/A
Answers
Answer:
(90+7)^{3} (xy)^{3}=912673x^{3} y^{3}(90+7)
3
(xy)
3
=912673x
3
y
3
Step-by-step explanation:
Since we need to expand (97xy)^3 using identity
So, we are expanding the given relation as follow
(97xy)^{3} =97^{3} (xy)^{3}=(90+7)^{3} (xy)^{3}(97xy)
3
=97
3
(xy)
3
=(90+7)
3
(xy)
3
...................(1)
since we know the identity
(a+b)^{3}=a^{3} +b^{3}+3ab(a+b)=a^{3} +b^{3}+3ab^{2} +3ba^{2}(a+b)
3
=a
3
+b
3
+3ab(a+b)=a
3
+b
3
+3ab
2
+3ba
2
...........................(2)
Apply the above identity to expand only 97^{3}97
3
here a=90 and b=7
(90+7)^{3}=90^{3} +7^{3}+3\times 90\times 7^{2} +3\times 7\times 90^{2}(90+7)
3
=90
3
+7
3
+3×90×7
2
+3×7×90
2
(90+7)^{3}=729000+343+170100+13230=912673(90+7)
3
=729000+343+170100+13230=912673 ..................(3)
put (90+7)^{3}=912673(90+7)
3
=912673 .......in equation (1)
we get,
(90+7)^{3} (xy)^{3}=912673x^{3} y^{3}(90+7)
3
(xy)
3
=912673x
3
y
3