Expand (2 + x)" – (2 - x)" in ascending powers of x and simplify your result.
following. ( chapter is binomial theorem plss answer correctly no unnecessary answer)
Answers
Answer:
the answer is 2x
Step-by-step explanation:
(2+x)- (2-x)
=2+x-2+x
=2-2+x+x
=2x
Answer:
The expansion of the given expression in ascending powers of x is 160x+72x^3+2x^5
Therefore (2+x)^5-(2-x)^5=160x+72x^3+2x^5
Step-by-step explanation:
Given expression is (2+x)^5-(2-x)^5
To find the expansion of the given expression in ascending powers of x :
First find (2+x)^5
(2+x)^5=(2+x)^{2+3}
=(2+x)^2.(2+x)^3
=(2^2+2(2)(x)+x^2).(2^3+3(2)^2(x)+3(2)(x^2)+x^3)
=(4+4x+x^2).(8+12x+6x^2+x^3)
=4(8+12x+6x^2+x^3)+4x(8+12x+6x^2+x^3)+x^2(8+12x+6x^2+x^3)
=4(8)+4(12x)+4(6x^2)+4(x^3)+4x(8)+4x(12x)+4x(6x^2)+4x(x^3)+x^2(8)+x^2(12x)+x^2(6x^2)+x^2(x^3)
=32+48x+24x^2+4x^3+32x+48x^2+24x^3+4x^4+8x^2+12x^3+6x^4+x^5
=32+80x+80x^2+40x^3+10x^4+x^5
Therefore (2+x)^5=32+80x+80x^2+40x^3+10x^4+x^5
Similarly we can find (2-x)^5
(2-x)^5=(2-x)^{2+3}
=(2-x)^2.(2-x)^3
=(2^2-2(2)(x)+x^2).(2^3-3(2)^2(x)+3(2)(x^2)-x^3)
=(4-4x+x^2).(8-12x+6x^2-x^3)
=4(8-12x+6x^2-x^3)-4x(8-12x+6x^2-x^3)+x^2(8-12x+6x^2-x^3)
=4(8)+4(-12x)+4(6x^2)-4(-x^3)-4x(8)-4x(-12x)-4x(6x^2)-4x(-x^3)+x^2(8)+x^2(-12x)+x^2(6x^2)+x^2(-x^3)
=32-48x+24x^2+4x^3-32x+48x^2-24x^3+4x^4+8x^2-12x^3+6x^4-x^5
=32-80x+80x^2-32x^3+10x^4-x^5
Therefore (2-x)^5=32-80x+80x^2-32x^3+10x^4-x^5
Substituting the values in (2+x)^5-(2-x)^5 we get
(2+x)^5-(2-x)^5=32+80x+80x^2+40x^3+10x^4+x^5-(32-80x+80x^2-32x^3+10x^4-x^5)
=32+80x+80x^2+40x^3+10x^4+x^5-32+80x-80x^2+32x^3-10x^4+x^5
=160x+72x^3+2x^5
Therefore the expansion of the