Question

Simplify:
(1) (2a + 5)(3a - 2) + (a + 2)(20 - 3)
(ii) (3a + 2)(2a + 3) - (4a - 3)(2a - 1)
(iii) (2a + 3b)(3a + 4b) - (7a + 3b)(a + 2b)
(iv) (a? - 3a + 2)(5a - 2) - (3a + 4a - 5)(2a - 1)
(v) (2a - b + c)(a - 2b) - (3a + 2b - c)(2a - b)
(vi) (3a - 2)(2a - 1)(3a + 5)
(vii) (5 - a)(- 2a + 3)(4 - 3a)Simplify:
(1) (2a + 5)(3a - 2) + (a + 2)(20 - 3)
(ii) (3a + 2)(2a + 3) - (4a - 3)(2a - 1)
(iii) (2a + 3b)(3a + 4b) - (7a + 3b)(a + 2b)
(iv) (a? - 3a + 2)(5a - 2) - (3a + 4a - 5)(2a - 1)
(v) (2a - b + c)(a - 2b) - (3a + 2b - c)(2a - b)
(vi) (3a - 2)(2a - 1)(3a + 5)
(vii) (5 - a)(- 2a + 3)(4 - 3a​

Answer 1

Answer:

(i)(2a+5)(3a-2)+(a+2)(20-3)

=2a(3a-2)+5(3a-2)+(a+2)17

=6a²-4a+15a-10+17a+34

=6a²-4a+15a+17a-10+34

=6a²+28a+14

(ii) (3a+2)(2a+3)-(4a-3)(2a-1)

=3a(2a+3)+2(2a+3)-4a(2a-1)-3(2a-1)

=6a²+9a+4a+6-8a²+4a-6a+3

=6a²-8a²+9a+4a+4a-6a+6+3

=(-2a²)+11a+9

=2a²-11a-9

(iii)(2a+3b)(3a+4b)-(7a+3b)(a+2b)

=2a(3a+4b)+3b(3a+4b)-7a(a+2b)+3b(a+2b)

=6a²+8ab+9ab+12b²-7a²-14ab+3ab+6b²

=6a²-7a²+12b²+6b²+8ab+9ab-14ab+3ab

=(-a²)+18b²+6ab

=a²-18b²-6ab

(v)(2a-b+c)(a-2b)-(3a+2b-c)(2a-b)

=2a(a-2b)-b(a-2b)+c(a-2b)-3a(2a-b)+2b(2a-b)-c(2a-b)

=2a²-4ab-ab+2b²+ac-2bc-6a²+3ab+4ab-2b²-2ac+bc

=2a²-6a²+2b²-2b²-4ab-ab+3ab+4ab-2bc+bc+ac-2ac

=(-4a²)+2ab-bc-ac

=4a²-2ab+bc+ac

(vi)(3a-2)(2a-1)(3a+5)

=3a(2a-1)-2(2a-1)+2a(3a+5)-1(3a+5) +3a(3a-2)+5(3a-2)

=6a²-3a-4a+2+6a²+10a-3a-5+9a²-6a+15a-10

=6a²+6a²+9a²-3a-4a+10a-3a-6a+15a+2-5-10

=21a²+9a-13

(vii)(5-a)(-2a+3)(4-3a)

=5(-2a+3)-a(-2a+3)-2a(4-3a)+3(4-3a)+4(5-a) -3a(5-a)

=(-10a)+15+2a²-3a-8a+6a²+12-9a+20-4a-15a+3a²

=2a²+6a²+3a²-10a-3a-8a-9a-4a-15a+15+12+20

=11a²-49a+47