Question

(2a-3b+3c)(4a+2b-c):simplify​

Answer 1

Answer:

Solution :

Given, a+3b+4c+5d2a+3b−4c−5d=2a−3b+4c+5d2a−3b−4c+5da+3b+4c+5d2a+3b-4c-5d=2a-3b+4c+5d2a-3b-4c+5d

⇒(2a+3b)+(4c+5d)(2a+3b)−(4c+5d)=(2a−3b)+(4c−5d)(2a−3b)−(4c−5d)⇒(2a+3b)+(4c+5d)(2a+3b)-(4c+5d)=(2a-3b)+(4c-5d)(2a-3b)-(4c-5d)

⇒2a+3b4c+5d=2a−3b4c−5d⇒2a+3b2a−3b=4c+5d4c−5d⇒2a+3b4c+5d=2a-3b4c-5d⇒2a+3b2a-3b=4c+5d4c-5d

Using componendo and dividendo rule,

(2a+3b)+(2a−3b)(2a+3b)−(2a−3b)=(4c+5d)+(4c−5d)(4c+5d)−(4c−5d)(2a+3b)+(2a-3b)(2a+3b)-(2a-3b)=(4c+5d)+(4c-5d)(4c+5d)-(4c-5d)

⇒4a6b=8c10d⇒a3b=2c5d⇒4a6b=8c10d⇒a3b=2c5d

∴a:3b::2c:5d∴a:3b::2c:5d

So, a,3b, 2c and 5d are in proportion

Answer 2

Answer:

Step-by-step explanation:

(2a-3b+3c)(4a+2b-c)

with 2a -----

2a*4a=8a²,

2a*2b=4ab,

2a*-c=-2ac,

with -3b ----

-3b*4a=-12ab,

-3b*2b=-6b²,

-3b*-c=3bc,

with 3c -----

3c*4a=12ac,

3c*2b=6bc,

3c*-c=-3c².

(8a²+4ab+2ac-12ab-6b²+3bc+12ac+6bc-3c²)

(8a²-6b²-3c²+4ab-12ab+6bc+3bc+2ac+12ac)

(8a²-6b²-3c²-8ab+9bc+24ac)