Match each binomial with its factors. Tiles 16x2 − 1 (2x + 1)(2x − 1) 16x2 − 4 (2x + 3)(2x − 3) 16x2 + 1 4(2x + 1)(2x − 1) 4x2 −
1 answer:
You can do this in two ways. The easiest way using the special case formulas since these are perfect squares. Another would be multiplying the pairs and seeing what matches the other.
Here are the formulas for special cases:
1. (2x+1)(2x-1) This follows the third formula where a=2x and b = 1
2. <span>(2x + 3)(2x − 3) This also follows the third formula where a=2x and b = 3
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3. <span> 4(2x + 1)(2x − 1) This follows the third formula but the result should be multiplied by 4. We can do this by combining the pairs first before multiplying it by 4. The associative property of multiplication allows this.
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From here we can use the distributive property:
4. <span>(4x − 1)(4x + 1) This also uses the third formula where a= 4x and b= 1</span>
So let's match up the pairs with their results:
Here are the formulas for special cases:
1. (2x+1)(2x-1) This follows the third formula where a=2x and b = 1
2. <span>(2x + 3)(2x − 3) This also follows the third formula where a=2x and b = 3
</span>
3. <span> 4(2x + 1)(2x − 1) This follows the third formula but the result should be multiplied by 4. We can do this by combining the pairs first before multiplying it by 4. The associative property of multiplication allows this.
</span>
From here we can use the distributive property:
4. <span>(4x − 1)(4x + 1) This also uses the third formula where a= 4x and b= 1</span>
So let's match up the pairs with their results:
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Answer:
a= 6
b = 7
c = 8
d = 7
e = 6
Step-by-step explanation:
Notice that the bike is 6 feet above the ground to start with, so when it starts rolling, the green dot is exactly 6 feet from the ground, which gives a=6
when the distance covered by the bike is , (see first red dot in the attached image), the position of the green dot is exactly 1 foot added to 6 ft= 7 feet
so b = 7
when the distance covered is , now the green dot would be at the top of the wheel (second red dot in the attached image) which involves adding 2 feet to the original 6 feet. That is: c = 8
when the distance covered is , the green dot is at the position of the third red dot in the attached image., that it exactly one foot added to 6 feet = 7 ft which gives the value of d = 7
and finally, when the distance covered is . the green dot has completed a full circle and is now again in its lower position (nothing - zero) added to 6 feet = 6ft, giving e = 6.
