EXERCISE 12.2
Simplify combining like terms:
(i) 21b - 32 + 7b - 205
i) – Z2 + 13z2 - 5z + 773 - 157
ii) p- (p - 9-9-(q-p)
V) 3a - 2b - ab - (a - b + ab) + 3ab + b - a
V) 5xły – 5x2 + 3yx2 – 3y2 + x² - y2 + 8xy2 – 3y?
i) (3y2 + 5y - 4) – (8y - y2 - 4)
Answers
Answer:
a)21b–32+7b–20b
Answer: 21b–32+7b–20b
=21b+7b–20b–32
=28b–20b–32=8b–32
(b) –z2+13z2–5z+7z3–15z
Answer: -z2+13z2–5z+7z3–15z
=-z2+13z2–5z–15z+7z3
=12z2–20z+7z3
(c) p–(p–q)–q–(q–p)
Answer: p–(p–q)–q–(q–p)
=p–p+q–q–q+p
=p–p+p+q–q–q
=p–q
(d) 3a–2b–ab–(a–b+ab)+3ab+b–a
Answer: 3a–2b–ab–a+b–ab+3ab+b–a
=3a–a–a–2b+b+b–ab–ab+3ab
=3a–2a–2b+2b–2ab+3ab
=a+ab
(e) 5x2y–5x2+3yx2–3y2+x2–y2+8xy2–3y2
Answer: 5x2y–5x2+3yx2–3y2+x2–y2+8xy2–3y2
=5x2y+3x2y–5x2+x2–3y2–y2+8xy2
=8x2y–4x2–4y2+8xy2
(f) (3y2+5y–4)–(8y–y2–4)
Answer: (3y2+5y–4)–(8y–y2–4)
=3y2+5y–4–8y+y2+4
=3y2+y2+5y–8y–4+4
=4y2–3y
Answer:
21b – 32 + 7b – 206
Re-arranging the like terms, we get
216 + 7b – 206 – 32
= (21 + 7 – 20)b – 32
= 8b – 32 which is required.
-z2 + 13z2 – 5z – 15z
-z2 + 13z2 – 5z – 15zRe-arranging the like terms, we get
-z2 + 13z2 – 5z – 15zRe-arranging the like terms, we get7z3 – z2 + 13z2 – 5z + 5z – 15z
-z2 + 13z2 – 5z – 15zRe-arranging the like terms, we get7z3 – z2 + 13z2 – 5z + 5z – 15z= 7z3 + (-1 + 13)z2 + (-5 – 15)z
-z2 + 13z2 – 5z – 15zRe-arranging the like terms, we get7z3 – z2 + 13z2 – 5z + 5z – 15z= 7z3 + (-1 + 13)z2 + (-5 – 15)z= 7z3 + 12z2 – 20z which is required.
3a – 2b – ab – (a – b + ab) + 3ab + b – a
3a – 2b – ab – (a – b + ab) + 3ab + b – a= 3a – 2b – ab – a + b – ab + 3ab + b – a
3a – 2b – ab – (a – b + ab) + 3ab + b – a= 3a – 2b – ab – a + b – ab + 3ab + b – aRe-arranging the like terms, we get
3a – 2b – ab – (a – b + ab) + 3ab + b – a= 3a – 2b – ab – a + b – ab + 3ab + b – aRe-arranging the like terms, we get= 3a – a – a – 2b + b + b – ab – ab + 3ab
3a – 2b – ab – (a – b + ab) + 3ab + b – a= 3a – 2b – ab – a + b – ab + 3ab + b – aRe-arranging the like terms, we get= 3a – a – a – 2b + b + b – ab – ab + 3ab= a + ab which is required.
5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2
5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2Re-arranging the like terms, we get
5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2Re-arranging the like terms, we get5x2y + 3x2y + 8xy2 – 5x2 + x2 – 3y2 – y2 – 3y2
5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2Re-arranging the like terms, we get5x2y + 3x2y + 8xy2 – 5x2 + x2 – 3y2 – y2 – 3y2= 8x2y + 8xy2 – 4x2 – 7y2 which is required
(3y2 + 5y – 4) – (8y – y2 – 4)
= 3y2 + 5y – 4 – 8y + y2 + 4 (Solving the brackets)
Re-arranging the like terms, we get
= 3y2 + y2 + 5y – 8y – 4 + 4
= 4y2 – 3y which is required