Use the distributive property to solve these problems. Show all your work by factorising.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems by factorising:

1.

Identify the common factor.
$34 \times 48 + 34 \times 52$
Factor out the common factor, which is 34.
$34 \times (48 + 52)$
Perform the addition inside the parentheses.
$34 \times 100$
Perform the multiplication.
$\boxed{\text{3400}}$
2.
Identify the common factor.
$61 \times 87 - 61 \times 85$
Factor out the common factor, which is 61.
$61 \times (87 - 85)$
Perform the subtraction inside the parentheses.
$61 \times 2$
Perform the multiplication.
$\boxed{\text{122}}$
3.
Identify the common factor.
$128 \times 27 - 28 \times 27$
Factor out the common factor, which is 27.
$(128 - 28) \times 27$
Perform the subtraction inside the parentheses.
$100 \times 27$
Perform the multiplication.
$\boxed{\text{2700}}$
4.
Identify the common factor.
$693 \times 7 + 693 \times 3$
Factor out the common factor, which is 693.
$693 \times (7 + 3)$
Perform the addition inside the parentheses.
$693 \times 10$
Perform the multiplication.
$\boxed{\text{6930}}$
5.
Identify the common factor.
$\frac{8}{13} \times 125 + \frac{5}{13} \times 125$
Factor out the common factor, which is 125.
$\left(\frac{8}{13} + \frac{5}{13}\right) \times 125$
Perform the addition inside the parentheses.
$\left(\frac{8+5}{13}\right) \times 125$ $\left(\frac{13}{13}\right) \times 125$ $1 \times 125$
Perform the multiplication.
$\boxed{\text{125}}$
6.
Identify the common factor.
$\frac{22}{7} \times 10 + \frac{22}{7} \times 4$
Factor out the common factor, which is $\frac{22}{7}$ .
$\frac{22}{7} \times (10 + 4)$
Perform the addition inside the parentheses.
$\frac{22}{7} \times 14$
Perform the multiplication.
$22 \times \frac{14}{7}$ $22 \times 2$ $\boxed{\text{44}}$

Use the distributive property to solve these problems. Show all your work by factorising.

Step-by-step solution

Identify the common factor.

Factor out the common factor, which is 34.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 61.

Perform the subtraction inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 27.

Perform the subtraction inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 693.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 125.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is $\frac{22}{7}$ .

Perform the addition inside the parentheses.

Perform the multiplication.

Still stuck on this one?

More Mathematics Questions

Use the distributive property to solve these problems. Show all your work by factorising.

Step-by-step solution

Identify the common factor.

Factor out the common factor, which is 34.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 61.

Perform the subtraction inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 27.

Perform the subtraction inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 693.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 125.

Perform the addition inside the parentheses.

Perform the multiplication.

Identify the common factor.

Factor out the common factor, which is 227\frac{22}{7}722​.

Perform the addition inside the parentheses.

Perform the multiplication.

Still stuck on this one?

More Mathematics Questions

Factor out the common factor, which is $\frac{22}{7}$ .