abc + 2ba + 3ac, 4ca – 4ab + 2bca and 2ab – 3abc - 6ac
Answers
Answer:
(i) 3x + 8y + 7z + 6y + 4z – 2x + 3y – 4x + 6z
= 3x – 2x – 4x + 8y + 6y + 3y + 7z + 4z + 6z
= 3x – 6x + 17y + 17z
= - 3x + 17y + 17z
(ii) 3a + 5b + 2c + 2a + 3b – c + a + b + c
= 3a + 2a + a + 5b + 3b + b + 2c – c + c
= 6a + 9b + 3c – c = 6a + 9b + 2c
(iii) ) 4x2+ 8xy – 2y2 and 8xy – 5y2 + x2
4x2 + 8xy – 2y2 + 8xy – 5y2 + x2
= 4x2 + x2 + 8xy + 8xy – 2y2 – 5y2
= 5x2 + 16xy – 7y2
(iv) 9x2 – 6x + 7, 5 – 4x and 6 – 3x2
= 9x2 – 6x + 7 + 5 – 4x + 6 – 3x2
= 9x2 – 3x2 – 6x – 4x + 7 + 5 + 6
= 6x2 – 10x + 18
(v) 5x2 – 2xy + 3y2 and – 2x2 + 5xy + 9y2
and 3x2 - xy- 4y2
5x2 – 2xy + 3y2 – 2x2 + 5xy + 9y2 + 3x2 – xy – 4y2
= 5x2 – 2x2 + 3x2 – 2xy + 5xy – xy + 3y2 + 9y2 – 4y2
= 8x2 – 2x2 + 5xy – 3xy + 12y2 – 4y2
= 6x2 + 2xy + 8y2
(vi) a2 + b2 + 2ab, 2b2 + c2 + 2bc
and 4c2- a2 + 2ac
a2 + b2 + 2ab + 2b2 + c2 + 2bc + 4c2 - a2 + 2ac
= a2 – a2 + b2 + 2b2 + c2 + 4c2 + 2ab + 2bc + 2ac
= 3b2 + 5c2 + 2ab + 2bc + 2ac
(vii) 9ax – 6bx + 8, 4ax + 8bx – 7
and – 6ax – 46x – 3
9ax – 6bx – 8 + 4ax + 8bx – 7 – 6ax – 4bx – 3
= 9ax + 4ax – 6ax – 6bx + 8bx – 4bx + 8 – 7 – 3
= 13ax – 6ax + 8bx – 10bx + 8 – 10
= 7ax – 2bx – 2
(viii) abc + 2ba + 3 ac, 4ca – 4ab + 2 bca
and 2ab – 3abc – 6ac
abc + 2ab + 3ca + 4ca – 4ab + 2abc + 2ab – 3abc – 6ca
= abc + 2abc – 3abc + 2ab – 4ab + 2ab + 3ca + 4ca - 6ca
= 3abc – 3abc + 4ab – 4ab + 7ca – 6ca
= 0 + 0 + ca = ca
(ix) 4a2 + 5b2 – 6ab, 3ab, 6a2 – 2b2
and 4b2 – 5 ab
4a2 + 5b2 – 6ab + 3ab + 6a2 – 2b2 + 4b2 – 5ab
= 4a2 + 6a2 + 5b2 – 2b2 + 4b2 – 6ab + 3ab – 5ab
= 10a2 + 9b2 – 2b2 – 11ab + 3ab
= 10a2 + 7b2 – 8ab
(x) x2 + x – 2, 2x – 3x2 + 5 and 2x2 – 5x + 7
= x2 + x – 2 + 2x – 3x2 + 5 + 2x2 – 5x + 7
= x2 – 3x2 + 2x2 + x + 2x – 5x – 2 + 5 + 7
= 3x2 – 3x2 + 3x – 5x – 2 + 12
= 0 – 2x + 10
= - 2x + 10
(xi) 4x3 + 2x2 – x + 1, 2x3 – 5x2 – 3x + 6, x2 + 8 and 5x3 – 7x
4x3 + 2x2 – x + 1 + 2x3 – 5x2 – 3x + 6 + x2 + 8 + 5x3 – 7x
= 4x3 + 2x3 + 5x3 + 2x2 – 5x2 + x2 – x – 3x – 7x + 1 + 6 + 8
= 11x3 + 3x2 – 5x2 – 11x + 15
= 11x3 – 2x2 – 11x + 15