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

Skip to content# 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.

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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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