Question59. $6 d+4(3 d+5)$
62. $a+\frac{a}{5}+\frac{2}{5} a$
65. $7(2 x+y)+6(x+5 y)$

Studdy Solution

STEP 1

1. Each expression needs to be simplified.
2. Simplification involves distributing multiplication over addition and combining like terms.
3. The expressions are algebraic, involving variables and constants.

STEP 2

1. Simplify the expression $6d + 4(3d + 5)$ .
2. Simplify the expression $a + \frac{a}{5} + \frac{2}{5}a$ .
3. Simplify the expression $7(2x + y) + 6(x + 5y)$ .

STEP 3

Distribute the multiplication in the expression $6d + 4(3d + 5)$ :
$4(3d + 5) = 4 \times 3d + 4 \times 5 = 12d + 20$
The expression becomes:
$6d + 12d + 20$

STEP 4

Combine like terms:
$6d + 12d = 18d$
The simplified expression is:
$18d + 20$

STEP 5

Simplify the expression $a + \frac{a}{5} + \frac{2}{5}a$ :
Combine the terms with $a$ by finding a common denominator:
$a = \frac{5a}{5}$
Now, combine:
$\frac{5a}{5} + \frac{a}{5} + \frac{2a}{5} = \frac{5a + a + 2a}{5} = \frac{8a}{5}$
The simplified expression is:
$\frac{8a}{5}$

STEP 6

Distribute the multiplication in the expression $7(2x + y) + 6(x + 5y)$ :
$7(2x + y) = 7 \times 2x + 7 \times y = 14x + 7y$
$6(x + 5y) = 6 \times x + 6 \times 5y = 6x + 30y$
The expression becomes:
$14x + 7y + 6x + 30y$

STEP 7

Combine like terms:
$14x + 6x = 20x$
$7y + 30y = 37y$
The simplified expression is:
$20x + 37y$

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