Question

Can you answer these please many thanks

Answer 1

Given: (a)
`2(x+3)=2x+6` and (b)
`4(y-3)=4y-12`.

To find: The expanded form of the given expressions.

(c)
`4(m+n)=4m+4n` (using
`a(b+c)=ab+ac`)

(d)
`3(5-q)=15-3q` (using
`a(b-c)=ab-ac`)

(e)
`5(2c+1)=10c+5` (using
`a(b+c)=ab+ac`)

(f)
`3(2x-5)=6x-15` (using
`a(b-c)=ab-ac`)

(g)
`7(4b-1)=28b-7` (using
`a(b-c)=ab-ac`)

(h)
`3(2x+y-5)=3((2x+y)-5)`

⇒
`3(2x+y-5)=3(2x+y)-15` (using
`a(b-c)=ab-ac`)

⇒
`3(2x+y-5)=6x+3y-15` (using
`a(b+c)=ab+ac`)

(i)
`2(6a-4b+3)=2((6a-4b)+3)`

⇒
`2(6a-4b+3)=2(6a-4b)+6` (using
`a(b+c)=ab+ac`)

⇒
`2(6a-4b+3)=12a-8b+6` (using
`a(b-c)=ab-ac`)

(j)
`6(m+n+p)=6((m+n)+p)`

⇒
`6(m+n+p)=6(m+n)+6p` (using
`a(b+c)=ab+ac`)

⇒
`6(m+n+p)=6m+6n+6p` (using
`a(b+c)=ab+ac`)

(k)
`y(y+2)=y^2+2y` (using
`a(b+c)=ab+ac`)

(l)
`g(g-3)=g^2-3g` (using
`a(b-c)=ab-ac`)

(m)
`n(4-n)=4n-n^2` (using
`a(b-c)=ab-ac`)

(n)
`a(b+c)=ab+ac` (using
`a(b+c)=ab+ac`)

(o)
`s(3s-4)=3s^2-4s` (using
`a(b-c)=ab-ac`)

(p)
`2x(x+5)=2x^2+10x` (using
`a(b+c)=ab+ac`)

(q)
`4y(x-3)=4xy-12y` (using
`a(b-c)=ab-ac`)

(r)
`5a(2b-5)=10ab-25a` (using
`a(b-c)=ab-ac`)

(s)
`4a(3b+2c)=12ab+8ac` (using
`a(b+c)=ab+ac`)

(t)
`5p(4p-5q)=20p^2-25pq` (using
`a(b-c)=ab-ac`)