Q.1 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 + 6 – a
\( (v) 5x^2y – 5x^2 + 3yx^2 – 3y^2 + x^2 – y^2 + 8xy^2 -3y^2 \)
\((vi) (3y^2 + 5y – 4) – (8y – y^2 – 4) \)


Answer :

(i) 21b – 32 + 7b – 20b
= 21b + 7b -20b -32
= 8b -32
(ii) \(-z^2 + 13z^2 -5z + 7z^3 – 15z \)
= \(-z^2 + 13z^2 -5z - 15z + 7z^3 \)
= \( 11z^2 -20z + 7z^3 \)
(iii) ( p – (p – q) – q – (q – p)
= p-p +q-q-q+p
= p- q
(iv) 3a – 2b — ab – (a – b + ab) + 3ab + 6 – a
= 3a - 2b - ab - a + b - ab +3ab + 6 - a
= 3a – a – a – 2b + b + b – ab – ab + 3ab
= a +ab
(v) \( 5x^2y – 5x^2 + 3yx^2 – 3y^2 + x^2 – y^2 + 8xy^2 -3y^2 \)
= \( 5x^2y + 3yx^2 – 5x^2 + x^2 – 3y^2 – y^2 – 3y^2+ 8xy^2 \)
= 8x^2y – 4x^2 – 7y^2 + 8xy^2
(vi) \( (3y^2 + 5y – 4) – (8y – y^2 – 4) \)
= \( 3y^2 + 5y – 4 – 8y + y^2 + 4) \)
= \( 3y^2 + y^2 + 5y – 8y – 4 + 4 \)
= \( 4y^2 – 3y \)

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