Question

verify x(y+z)=xy+xz for x= -5/12, y=7/8 , z=-12/3​

Answer 1

GIVEN :

The values are $x=-\frac{5}{12}$ , $y=\frac{7}{8}$ and $z=-\frac{12}{3}$

TO VERIFY :

The Distributive property x(y+z)=xy+xz for the given values  $x=-\frac{5}{12}$ , $y=\frac{7}{8}$ and $z=-\frac{12}{3}$

SOLUTION :

Given expression is x(y+z)=xy+xz for the given values  $x=-\frac{5}{12}$ , $y=\frac{7}{8}$ and $z=-\frac{12}{3}$

Now verify x(y+z)=xy+xz for the given values  $x=-\frac{5}{12}$ , $y=\frac{7}{8}$ and $z=-\frac{12}{3}$

Taking LHS x(y+z)

Substitute the values we get,

$x(y+z)=-\frac{5}{12}(\frac{7}{8}+(-\frac{12}{3}))$

$=-\frac{5}{12}(\frac{7}{8}-4)$

$=-\frac{5}{12}(\frac{7-32}{8})$

$=-\frac{5}{12}(\frac{-25}{8})$

$=\frac{125}{96}$

∴ $x(y+z)=\frac{125}{96}\hfill (1)$ = LHS

Taking RHS xy+xz

Substitute the values we get,

$xy+xz=-\frac{5}{12}(\frac{7}{8})+(-\frac{5}{12})(-\frac{12}{3})$

$=-\frac{35}{96}+\frac{5}{3}$

$=\frac{-105+480}{288}$

$=\frac{375}{288}$

$=\frac{125}{96}$

∴ $xy+xz=\frac{125}{96}\hfill (2)$ = RHS

Comparing the equations (1) and (2) we get,

(1)=(2)

LHS=RHS

∴ the distributive property x(y+z)=xy+xz for the given values  $x=-\frac{5}{12}$ , $y=\frac{7}{8}$ and $z=-\frac{12}{3}$ is verified.

Answer 2

Given:

x= -5/12,

y= 7/8,

z= -12/3​.

To verify:

x(y+z)=xy+xz

Solution:

1) To verify the above equation we have to solve the term side by side.

2) LHS

• x(y+z)

Putting the values of x, y and z.

• -5/12[7/8+(-12/3)]

• -5/12[7/8 - 4]

• -5/12[(7 - 32)/8]

• (-5/12)(-25/8)

• 125/96

3) RHS

• xy+xz

• (-5/12)(7/8) + (-5/12)(-12/3)

• -35/96 + 5/3

• (-35 + 160)/96

• 125/96

LHS = RHS

Hence verified.

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