Which of the following expressions is NOT equivalent to (a + b)(x + y) ?
a. (a + b)x + (a + b)y
b. a(x + y) + b(x + y)
c. (b + a)(y + x)
d. ax + by
e. ax + bx + ay + by
d. ax + by
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To determine which of the following expressions is NOT equivalent to (a + b)(x + y), we can expand the original expression and compare it with the given options.
Expanding (a + b)(x + y) using the distributive property, we get:
(a + b)(x + y) = ax + ay + bx + by
Now, let's compare it with the given options:
a. (a + b)x + (a + b)y
Expanding this option, we get ax + bx + ay + by, which is equivalent to the original expression. So, option a is not the answer.
b. a(x + y) + b(x + y)
Expanding this option, we get ax + ay + bx + by, which is equivalent to the original expression. So, option b is not the answer.
c. (b + a)(y + x)
Expanding this option, we get by + ay + bx + ax. This expression is equivalent to the original expression since addition is commutative. So, option c is not the answer.
d. ax + by
This option does not include the term ay, so it is not equivalent to the original expression. Therefore, option d is the answer.
e. ax + bx + ay + by
Expanding this option, we get ax + bx + ay + by, which is equivalent to the original expression. So, option e is not the answer.
In conclusion, the expression that is NOT equivalent to (a + b)(x + y) is option d.