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8. Find the product using suitable properties:

(a) [tex]26 \times (-48) + (-48) \times (-36)[/tex]

(b) [tex]8 \times 53 \times (-125)[/tex]

(c) [tex]15 \times (-25) \times (-4) \times (-10)[/tex]

(d) [tex](-41) \times 102[/tex]

(e) [tex]625 \times (-35) + (-625) \times 65[/tex]

(f) [tex]7 \times (50 - 2)[/tex]

(g) [tex](-17) \times (-29)[/tex]

(h) [tex](-57) \times (-19) + 57[/tex]

Sagot :

GinnyAnswer
Sure! Let's find the products step by step using suitable properties:

### Part (a)
[tex]\[ 26 \times (-48) + (-48) \times (-36) \][/tex]

1. Calculate \( 26 \times (-48) \):
[tex]\[ 26 \times (-48) = -1248 \][/tex]

2. Calculate \( (-48) \times (-36) \):
[tex]\[ (-48) \times (-36) = 1728 \][/tex]

3. Sum the results:
[tex]\[ -1248 + 1728 = 480 \][/tex]

### Part (b)
[tex]\[ 8 \times 53 \times (-125) \][/tex]

1. Multiply the numbers:
[tex]\[ 8 \times 53 \times (-125) = -53000 \][/tex]

### Part (c)
[tex]\[ 15 \times (-25) \times (-4) \times (-10) \][/tex]

1. Multiply the numbers in order:
[tex]\[ 15 \times (-25) = -375 \][/tex]
[tex]\[ -375 \times (-4) = 1500 \][/tex]
[tex]\[ 1500 \times (-10) = -15000 \][/tex]

### Part (d)
[tex]\[ (-41) \times 102 \][/tex]

1. Multiply the numbers:
[tex]\[ (-41) \times 102 = -4182 \][/tex]

### Part (e)
[tex]\[ 625 \times (-35) + (-625) \times 65 \][/tex]

1. Calculate \( 625 \times (-35) \):
[tex]\[ 625 \times (-35) = -21875 \][/tex]

2. Calculate \( (-625) \times 65 \):
[tex]\[ (-625) \times 65 = -40625 \][/tex]

3. Sum the results:
[tex]\[ -21875 + (-40625) = -62500 \][/tex]

### Part (f)
[tex]\[ 7 \times (50 - 2) \][/tex]

1. Calculate inside the parenthesis:
[tex]\[ 50 - 2 = 48 \][/tex]

2. Multiply the result by 7:
[tex]\[ 7 \times 48 = 336 \][/tex]

### Part (g)
[tex]\[ (-17) \times (-29) \][/tex]

1. Multiply the numbers:
[tex]\[ (-17) \times (-29) = 493 \][/tex]

### Part (h)
[tex]\[ (-57) \times (-19) + 57 \][/tex]

1. Calculate \( (-57) \times (-19) \):
[tex]\[ (-57) \times (-19) = 1083 \][/tex]

2. Add 57 to the result:
[tex]\[ 1083 + 57 = 1140 \][/tex]

So, the solutions are:
(a) 480
(b) -53000
(c) -15000
(d) -4182
(e) -62500
(f) 336
(g) 493
(h) 1140
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