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secondary 2 | Maths
4 Answers Below
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Date Posted: 3 years ago
Views: 319
5×(88²-144)
= 5×(88²-12²)
= 5×(88+12)(88-12)
= 500×76
= 38000
= 5×(88²-12²)
= 5×(88+12)(88-12)
= 500×76
= 38000
Should be 38000 instead of 3800
5 × (88 + 12)(88 - 12)
= 5 × 100 × 76
= 5 × 76 × 100
= 380 × 100
= 38000
5 × (88 + 12)(88 - 12)
= 5 × 100 × 76
= 5 × 76 × 100
= 380 × 100
= 38000
Alternative working :
5 × 88² - 720
= 5 × (80 + 8)² - 720
= 5 × (80² + 2(80)(8) + 8²) - 720
= 5 × 80 × 80 + 5 × 2 × 8 × 80 + 5 × 8 × 8 - 720
= 400 × 80 + 80 × 80 + 40 × 8 - 720
= 32000 + 6400 + 320 - 720
= 32000 + 6400 - 400
= 32000 + 6000
= 38000
5 × 88² - 720
= 5 × (80 + 8)² - 720
= 5 × (80² + 2(80)(8) + 8²) - 720
= 5 × 80 × 80 + 5 × 2 × 8 × 80 + 5 × 8 × 8 - 720
= 400 × 80 + 80 × 80 + 40 × 8 - 720
= 32000 + 6400 + 320 - 720
= 32000 + 6400 - 400
= 32000 + 6000
= 38000
Second alternative :
Alternative working :
5 × 88² - 720
= 5 × (90 - 2)² - 720
= 5 × (90² - 2(90)(2) + 2²) - 720
= 5 × 90 × 90 - 5 × 2 × 2 × 90 + 5 × 2 × 2 - 720
= 5 × 8100 - 10 × 180 + 20 - 720
= 40500 - 1800 - 700
= 40500 - 2500
= 38000
Alternative working :
5 × 88² - 720
= 5 × (90 - 2)² - 720
= 5 × (90² - 2(90)(2) + 2²) - 720
= 5 × 90 × 90 - 5 × 2 × 2 × 90 + 5 × 2 × 2 - 720
= 5 × 8100 - 10 × 180 + 20 - 720
= 40500 - 1800 - 700
= 40500 - 2500
= 38000
Third alternative :
5 × 88² - 720
= 5 × (100 - 12)² - 720
= 5 × (100² - 2(100)(12) + 12²) - 720
= 5 × 100 × 100 - 5 × 2 × 12 × 100 + 5 × 12 × 12 - 720
= 5 × 10000 - 10 × 1200 + 60 × 12 - 720
= 50000 - 12000 + 720 - 720
= 38000
5 × 88² - 720
= 5 × (100 - 12)² - 720
= 5 × (100² - 2(100)(12) + 12²) - 720
= 5 × 100 × 100 - 5 × 2 × 12 × 100 + 5 × 12 × 12 - 720
= 5 × 10000 - 10 × 1200 + 60 × 12 - 720
= 50000 - 12000 + 720 - 720
= 38000
See 4 Answers
Most straightforward way is to use the property a² - b² = (a - b)(a + b)
First, factorise 720. Rewrite it as a multiple of 5 so we can group it together with the other term.
5 × 88² - 720 = 5 × 88² - 5 × 144 = 5 × (88² - 144)
Next, realise that 144 is a square number. 144 = 12 × 12 = 12² (you should know your multiplication table up to 12 pretty well)
= 5 × (88² - 12²)
Here is where you use the property mentioned above.
= 5 × (88 - 12)(88 + 12)
= 5 × (76)(100)
Now you have a very nice result so just multiply 5 by 76 first
= 380 × 100
= 38000 (×100 is simply adding two 0's behind)
First, factorise 720. Rewrite it as a multiple of 5 so we can group it together with the other term.
5 × 88² - 720 = 5 × 88² - 5 × 144 = 5 × (88² - 144)
Next, realise that 144 is a square number. 144 = 12 × 12 = 12² (you should know your multiplication table up to 12 pretty well)
= 5 × (88² - 12²)
Here is where you use the property mentioned above.
= 5 × (88 - 12)(88 + 12)
= 5 × (76)(100)
Now you have a very nice result so just multiply 5 by 76 first
= 380 × 100
= 38000 (×100 is simply adding two 0's behind)
done
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Date Posted:
3 years ago
done
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Date Posted:
3 years ago
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Date Posted:
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