Answer.
a^2+4a+16
a^2+15a+75
a^2+14a+49
a^2+26a+169
which expressions are differences of squares?
select each correct answer.
a^2−36
x^2+25
w^2−121
n^2−50
Answer.
a^2+4a+16
a^2+15a+75
a^2+14a+49
a^2+26a+169
which expressions are differences of squares?
select each correct answer.
a^2−36
x^2+25
w^2−121
n^2−50
Whaaa how old are you this is hard boy
A²-b² is difference
A. t²-1², yep
B. nope, not difference
C. n²-15²,yep
D. we can force it but I wouldn''t pick this one
A and C
Step-by-step explanation:
[tex]Which expressions are differences of squares? select each correct answer. h2−20 t2−4 x2−169 a2+1[/tex]
The correct options are 3 and 4.
Step-by-step explanation:
The difference of squares is defined as
[tex]a^2-b^2[/tex]
In option 1,
[tex]k^2+81[/tex]
It can be written as
[tex]k^2+9^2[/tex]
It is the sum of squares, therefore the option 1 is incorrect.
In option 2,
[tex]P^2-40[/tex]
The number 40 is not a complete square of any number, therefore option 2 is incorrect.
In option 3,
[tex]n^2-225[/tex]
It can be rewritten as
[tex]n^2-(15)^2[/tex]
It is the difference of squares, therefore option 3 is correct.
In option 4,
[tex]t^2-1[/tex]
It can be rewritten as
[tex]t^2-1^2[/tex]
It is the difference of squares, therefore option 4 is correct.
Step-by-step explanation:
[tex]Which expressions are differences of squares? select each correct answer. h2−20 t2−4 x2−169 a2+1[/tex]
1. the perfect squares in this case are
a²+26a+169 = (a+13)²
a²+14a+49 = (a+7)²
2. factorising
4p²+36p+81
product = 324
sum = 36
numbers are 18 and 18
Thus , 4p²+18p+18p+81
2p(2p+9) +9p(2p+9)
thus, (2p+9p)(2p+9p)
3. Factor 81a36-64b16
this is the difference between two squares, such that;
a²-b² = (a+b)(a-b)
therefore, 81a36 -64b16 will be;
(9a18-8b8)(9a18+8b8)
4. The differences between two squares is such that;
a²-b² = (a+b)(a-b)
therefore in this case, the difference between two squares will be;
x²-169 = (a-13)(a+13), and
t²-4 = (t-4)(t+4)
A and B
Because t^2-(1)^2
(n)^2-(15)^2
Option B, C and D are correct.
[tex]a^2-36[/tex], [tex]w^2-121[/tex] and [tex]n^2-50[/tex]
Step-by-step explanation:
For any real number a and b:
Difference of square is given by:
[tex]a^2-b^2 = (a-b)(a+b)[/tex]
We have to find Which expressions are differences of squares.
Option A :
[tex]x^2+25[/tex]
⇒[tex]x^2+5^2[/tex]
This cannot be written as a difference of square.
Option B:
[tex]a^2-36[/tex]
⇒[tex]a^2-6^2[/tex]
⇒[tex](a-6)(a+6)[/tex]
Option C:
[tex]w^2-121[/tex]
⇒[tex]w^2-11^2[/tex]
⇒[tex](w-11)(w+11)[/tex]
Option D:
[tex]n^2-50[/tex]
⇒[tex]n^2-(\sqrt{50})^2[/tex]
⇒[tex](n-\sqrt{50})(n+\sqrt{50})[/tex]
Therefore, the expressions which are are differences of squares are:
[tex]a^2-36[/tex], [tex]w^2-121[/tex] and [tex]n^2-50[/tex]
Step-by-step explanation:
1. the perfect squares in this case are
a²+26a+169 = (a+13)²
a²+14a+49 = (a+7)²
First and fourth option are correct.
2. factorise 4p²+36p+81
Product = 324 and sum = 36
numbers are 18 and 18
∴ 4p²+18p+18p+81
⇒ 2p(2p+9) +9(2p+9)
⇒ (2p+9)(2p+9) ⇒ [tex](2p+9)^2[/tex]
3. Factor [tex]81a^36-64b^16[/tex]
As [tex]a^2-b^2=(a+b)(a-b)[/tex]
∴ [tex]81a^36-64b^16=(9a^18)^2-(8b^8)^2[/tex]
=[tex](9a^18-8b^8)(9a^18+8b^8)[/tex] (Option B)
4. The differences between two squares is such that;
a²-b² = (a+b)(a-b)
[tex]x^2-169=x^2-13^2=(a-13)(a+13)[/tex], and
[tex]t^2-4=t^2-2^2=(t-2)(t+2)[/tex]
First and third option correct.
A and C are correct because they can be factorized to get (a+6)(a-6) and (w+11)(w-11) while B and D can't be factorized to get those
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