Question

(2/3x+4)(3/2x+6)-(1/7x-1)(1/7x+1)​

Answer 1

Step-by-step explanation:

Answer:

\dfrac{(8x + 35) (6x + 35)}{49}

49

(8x+35)(6x+35)

Step-by-step explanation:

(\dfrac{2}{3}x + 4)( \dfrac{3}{2}x + 6) - (\dfrac{1}{7}x - 1)(\dfrac{1}{7}x + 1)(

3

2

x+4)(

2

3

x+6)−(

7

1

x−1)(

7

1

x+1)

Expand:

= (\dfrac{2}{3}x)(\dfrac{3}{2}x) + (\dfrac{2}{3}x)(6) + 4(\dfrac{3}{2}x) + 4(6) - [ (\dfrac{1}{7}x)^2 - (1)^2]=(

3

2

x)(

2

3

x)+(

3

2

x)(6)+4(

2

3

x)+4(6)−[(

7

1

x)

2

−(1)

2

]

Evaluate each term:

= x^2 + 4x + 6x + 24 - \dfrac{1}{49}x^2 +1=x

2

+4x+6x+24−

49

1

x

2

+1

Combine like terms:

= \dfrac{48}{49}x^2 + 10x + 25=

49

48

x

2

+10x+25

Put into single fraction:

= \dfrac{48x^2 + 490x + 1225}{49}=

49

48x

2

+490x+1225

Factorise:

= \dfrac{(8x + 35) (6x + 35)}{49}=

49

(8x+35)(6x+35)