Question

Can someone please help me with an Algebra 1 question for a medal and fan?

Answer 1

Find the product of (x - 7)squared

Answer 2

Sorry, but I don't understand

Answer 3

This means that when you say (x-7)^2

Answer 4

you haveto times x-7 by itself

Answer 5

LET US BEGIN by learning about the square numbers. They are the numbers
1· 1 2· 2 3· 3
and so on. The following are the first ten square numbers -- and their roots.
Square numbers 1 4 9 16 25 36 49 64 81 100
Square roots 1 2 3 4 5 6 7 8 9 10
1 is the square of 1. 4 is the square of 2. 9 is the square of 3. And so on.
The square root of 1 is 1. The square root of 4 is 2. The square root of 9 is 3. And so on.
In a multiplication table, the square numbers lie along the diagonal.
The square of a binomial
(a + b)2
The square of a binomial comes up so often that the student should be able to write the final product immediately. It will turn out to be a very specific trinomial. To see that, let us square (a + b):
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2.
For, the outers plus the inners will be
ab + ba = 2ab.
The order of factors does not matter.
(a + b)2 = a2 + 2ab + b2
The square of any binomial produces the following three terms:
1. The square of the first term of the binomial: a2
2. Twice the product of the two terms: 2ab
3. The square of the second term: b2
The square of every binomial has that form: a2 + 2ab + b2.
To recognize that is to know an essential product in the "multiplication table" of algebra.
(See Lesson 8 of Arithmetic: How to square a number mentally, particularly the square of 24, which is the "binomial" 20 + 4.)
Example 1. Square the binomial (x + 6).
Solution. (x + 6)2 = x2 + 12x + 36
x2 is the square of x.
12x is twice the product of x with 6. (x· 6 = 6x. Twice that is 12x.)
36 is the square of 6.
x2 + 12x + 36 is called a perfect square trinomial. It is the square of a binomial.
Example 2. Square the binomial (3x − 4).
Solution. (3x − 4)2 = 9x2 − 24x + 16
9x2 is the square of 3x.
−24x is twice the product of 3x· −4. (3x· −4 = −12x. Twice that is −24x.)
16 is the square of −4.
Note: If the binomial has a minus sign, then the minus sign appears only in the middle term of the trinomial. Therefore, using the double sign ± ("plus or minus"), we can state the rule as follows:
(a ± b)2 = a2 ± 2ab + b2
This means: If the binomial is a + b, then the middle term will be +2ab; but if the binomial is a − b, then the middle term will be −2ab
The square of +b or −b, of course, is always positive. It is always +b2.
Example 3. (5x3 − 1)2 = 25x6 − 10x3 + 1
25x6 is the square of 5x3. (Lesson 13: Exponents.)
−10x3 is twice the product of 5x3· −1. (5x3· −1 = −5x3. Twice that is −10x3.)
1 is the square of −1.
The student should be clear that (a + b)2 is not a2 + b2, any more than (a + b)3 is equal to a3 + b3.
An exponent may not be "distributed" over a sum.
(See Topic 25 of Precalculus: The binomial theorem.)
Example 4. Is this a perfect square trinomial: x2 + 14x + 49 ?
Answer. Yes. It is the square of (x + 7).
x2 is the square of x. 49 is the square of 7. And 14x is twice the product of x· 7.
In other words, x2 + 14x + 49 could be factored as
x2 + 14x + 49 = (x + 7)2
Note: If the coefficient of x had been any number but 14, this would not have been a perfect square trinomial.
Example 5 Is this a perfect square trinomial: x2 + 50x + 100 ?
Answer. No, it is not. Although x2 is the square of x, and 100 is the square of 10, 50x is not twice the product of x· 10. (Twice their product is 20x.)
Example 6 Is this a perfect square trinomial: x8 − 16x4 + 64 ?
Answer. Yes. It is the perfect square of x4 − 8.
Problem 1. Which numbers are the square numbers?
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Do the problem yourself first!

1, 4, 9, 16, 25, 36, 49, 64, etc.

They are the numbers 12, 22, 32, and so on.

Answer 6

sorry wrong one lol