Question

Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 4(x 2y 4)

1. Expression (C) 4x + 8y + 27 will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4).

### What is the Distributive Property?

• The distributive property of binary operations in mathematics generalizes the distributive law, which states that equality is always true in elementary algebra.
• In elementary arithmetic, for example, one has according to one, multiplication distributed over addition.
To find which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4):
• The Distributive Property says that:
a · (b + c) = a · b + a · c
Applying the Distributive property to the expression:
• 4 (x + 2y + 4)
We get:
• 4 (x + 2y + 4) = 4 · x + 4 · 2y + 4 · 4 = 4x + 8y + 16
Hence,
• 11 + 4(x + 2y + 4) = 11x + 4x + 8y + 16
There are only two like terms 11 and 16, combining them we’ll get:
• 11 + 4(x + 2y + 4) = 11x + 4x + 8y + 16
• = (11 + 16) + 4x + 8y = 27 + 4x + 8y
Therefore, expression (C) 4x + 8y + 27 will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4).
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The correct question is given below:
Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?
(A) 4x + 2y + 27
(B) 4x + 8y + 11
(C) 4x + 8y + 27
(D) 4x + 8y + 10