which expressions are equivalent to 4(4a + 5)? choose 3 answers: a 16a + 5 b 16a + 20 c 12a + 20 + 4a d 2(8a…
which expressions are equivalent to 4(4a + 5)? choose 3 answers: a 16a + 5 b 16a + 20 c 12a + 20 + 4a d 2(8a + 10) e 16a + 5 + 4
Answer
Explanation:
Step1: Expand the original expression
Use the distributive property (c(a + b)=ca+cb). Here (c = 4), (a = 4a), (b = 5), so (4(4a + 5)=4\times4a+4\times5=16a + 20).
Step2: Analyze option B
Option B is (16a + 20), which is equal to the expanded - form of the original expression.
Step3: Analyze option C
Simplify (12a + 20+4a) by combining like - terms. (12a+4a+20=(12 + 4)a+20=16a + 20), which is equal to the original expression.
Step4: Analyze option D
Expand (2(8a + 10)) using the distributive property: (2\times8a+2\times10 = 16a+20), which is equal to the original expression.
Step5: Analyze option A
(16a + 5\neq16a + 20), so option A is not equivalent.
Step6: Analyze option E
Simplify (16a+5 + 4=16a+9\neq16a + 20), so option E is not equivalent.
Answer:
B. (16a + 20) C. (12a + 20 + 4a) D. (2(8a + 10))