Which trinomials are perfect square trinomials? select each correct answer. a2+26a+169 a2+4a+16 a2+14a+49 a2+15a+75 factor completely. 4p² + 36p + 81 express the answer in the form (ap+b)2 . enter your answer in the box. factor. 81a36−64b16 (9a6−8b4)(9a6+8b4) (9a18−8b8)(9a18+8b8) (9a6−8b4)2 (9a18−8b8)2 which expressions are differences of squares? select each correct answer. x2−169 h2−20 t2−4 a2+1

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) ⇒

3. Factor

As

∴  

                                   =  (Option B)

4.  The differences between two squares is such that;

a²-b² = (a+b)(a-b)

, and

First and third option correct.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)