clarification of model in regression

# we have to clarification of Y=A+B+(A*B) Is same or not Y=(A*B) 

 # Here i have taken one data set is related to cars and i assume Y is mpg as dependent
 
# And  A is first And B is second independent variable 

 library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

 data(mtcars)
 class(mtcars)

## [1] "data.frame"

 d=mtcars
 View(mtcars)
 y=d$mpg
 A=d$disp
 B=d$hp

 reg1=lm(y~A+B+(A*B))
 reg1

## 
## Call:
## lm(formula = y ~ A + B + (A * B))
## 
## Coefficients:
## (Intercept)            A            B          A:B  
##    39.67426     -0.07337     -0.09789      0.00029

 summary(reg1)

## 
## Call:
## lm(formula = y ~ A + B + (A * B))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5153 -1.6315 -0.6346  0.9038  5.7030 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.967e+01  2.914e+00  13.614 7.18e-14 ***
## A           -7.337e-02  1.439e-02  -5.100 2.11e-05 ***
## B           -9.789e-02  2.474e-02  -3.956 0.000473 ***
## A:B          2.900e-04  8.694e-05   3.336 0.002407 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.692 on 28 degrees of freedom
## Multiple R-squared:  0.8198, Adjusted R-squared:  0.8005 
## F-statistic: 42.48 on 3 and 28 DF,  p-value: 1.499e-10

 reg2=lm(y~(A*B))
 reg2

## 
## Call:
## lm(formula = y ~ (A * B))
## 
## Coefficients:
## (Intercept)            A            B          A:B  
##    39.67426     -0.07337     -0.09789      0.00029

 summary(reg2)

## 
## Call:
## lm(formula = y ~ (A * B))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5153 -1.6315 -0.6346  0.9038  5.7030 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.967e+01  2.914e+00  13.614 7.18e-14 ***
## A           -7.337e-02  1.439e-02  -5.100 2.11e-05 ***
## B           -9.789e-02  2.474e-02  -3.956 0.000473 ***
## A:B          2.900e-04  8.694e-05   3.336 0.002407 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.692 on 28 degrees of freedom
## Multiple R-squared:  0.8198, Adjusted R-squared:  0.8005 
## F-statistic: 42.48 on 3 and 28 DF,  p-value: 1.499e-10

## Conclsuion: here both reg1 is Y=A+B+(A*B) is same as reg2 is  Y=(A*B) it can be get 
## of summary same for both regression is same hence both is same.