Ncert solutions

# Question 1

Q1) Simplify combining like terms:

i) 21b-32+7b-20b

ii) -z^2+13z^2-5z+7z^3-15z

iii) p-(p-q)-q-(q-p)

iv) 3a-2b-ab-(a-b+ab)+3ab+b-a

v) 5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2

vi) (3y2+5y-4)-(8y-y2-4)

Solution i) 21b-32+7b-20b

Now, we re-arrange the like terms which gives us

= 21b\ +\ 7b\ -\ 20b\ -\ 32

= b\left(21\ +\ 7\ -\ 20\right)\ -\ 32

= 8b\ -\ 32

Solution ii) -z^2+13z^2-5z+7z^3-15z

Now, we re-arrange the like terms which give us

= 7z^{3\ }+z^2\ +\ 13z^2\ -\ 5z\ +\ 5z\ -\ 15z

= 7z^3\ +\ \left(-1\ +\ 13\right)\ z^2\ +\ \left(-5\ -\ 15\right)z

= 7z^3\ +\ 12z^2\ -\ 20z

Solution iii) p-(p-q)-q-(q-p)

Now, we re-arrange the like terms which give us

= p\ -p\ +\ q\ -q\ -q\ +\ p

After simplifying, we get

= p-q

Solution iv) 3a-2b-ab-(a-b+ab)+3ab+b-a

Now, we re-arrange the like terms which give us

= 3a\ -2b-ab\ -\ a\ +\ b\ -ab\ +\ 3ab\ +b\ -a

= 3a\ -\ a\ -a\ -2b\ +\ b\ +b\ -ab\ -ab\ +3ab

After simplifying, we get

= 3a\ -\ 2a\ -2ab\ +\ 3ab

= a\ +\ ab

Solution v) 5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2

Now, we re-arrange the llike terms which give us

=5x^2y\ +\ 3x^2y\ +\ 8xy^2\ -\ 5x^{2\ }+\ x^{2\ }-\ 3y^2\ -\ y^2\ -\ 3y^2

= 8x^2y\ +\ 8xy^2\ -4x^2\ -\ 7y^2

Solution vi) (3y2+5y-4)-(8y-y2-4)

Now, we re-arrange the like terms which give us

= 3y^2\ +\ 5y\ -\ 4\ -\ 8y\ -\ y^2\ -\ 4

After simplifying, we get

4y^{2\ }-\ 3y

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