QuestionIdentify equivalent expressions to $4(4 a+5)$ . Select 3: $16 a+5$ , $16 a+20$ , $12 a+20+4 a$ , $2(8 a+10)$ , $16 a+5+4$ .

Studdy Solution

STEP 1

Assumptions1. The expression to be evaluated is $4(4 a+5)$ . We are looking for expressions that are equivalent to the given expression

STEP 2

First, we need to simplify the given expression. We can do this by applying the distributive property of multiplication over addition.
$4(4 a+5) =4 \\times4a +4 \\times5$

STEP 3

Now, multiply the values to simplify the expression.
$\\timesa + \\times5 =16a +20$

STEP 4

Now, we need to compare the simplified expression $16a +20$ with each of the given options.

STEP 5

First, compare the simplified expression with the first option $16 a+5$ . $16a +20 \neq16 a+5$ So, the first option is not equivalent to the given expression.

STEP 6

Next, compare the simplified expression with the second option $16 a+20$ .
$16a +20 =16 a+20$ So, the second option is equivalent to the given expression.

STEP 7

Now, compare the simplified expression with the third option $12 a+20+4 a$ .
First, simplify the third option by combining like terms.
$12 a+20+4 a =16a +20$ Now, compare the simplified third option with the simplified expression.
$16a +20 =16a +20$ So, the third option is equivalent to the given expression.

STEP 8

Next, compare the simplified expression with the fourth option $2(8 a+10)$ .
First, simplify the fourth option by applying the distributive property of multiplication over addition.
$2(8 a+10) =2 \\times8a +2 \\times10 =16a +20$ Now, compare the simplified fourth option with the simplified expression.
$16a +20 =16a +20$ So, the fourth option is equivalent to the given expression.

STEP 9

Finally, compare the simplified expression with the fifth option $16 a+5+4$ .
First, simplify the fifth option by combining like terms.
$16 a+5+4 =16a +9$ Now, compare the simplified fifth option with the simplified expression.
$16a +20 \neq16a +9$ So, the fifth option is not equivalent to the given expression.

STEP 10

After comparing all the options, we find that the expressions equivalent to $4(4 a+5)$ are $16 a+20$ , $12 a+20+4 a$ , and $2(8 a+10)$ .

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