factor the perfect square trinomials 25y^4+70y^2z^2+49z^4

Question

please also tell me how you factored it out by showing a solution :) thank you

1. 25y^4+70y^2z^2+49z^4

2. 20a^5x^4-140a^4bx^3y+245a^3b^2x^2y^2

3. 9/4a^2-5ab+25/9b^2

Answer 1

25y^4 + 70y^2z^2 + 49z^4

(a + b)^2 = a^2 + 2ab + b^2

a^2 is our 25y^4, so a is 5y^2

b^2 is our 49z^4, so b is 7z^2

(5y^2 + 7z^2) ^ 2

.

20a^5x^4-140a^4bx^3y+245a^3b^2x^2y^2

5a^3x^2 ( 4a^2x^2 - 28axy + 49b^2y^2)

a^2 is like our 4a^2x^2, so a is like 2ax

b^2 is like our 49b^2y^2, so b is like 7by

5 a^3 x^2 ( 2ax + 7by )^2

.

(9/4)a^2 - 5ab + (25/9)b^2

a^2 is like our (9/4)a^2, so a is like (3/2)a

b^2 is like our (25/9)b^2, so b is like (5/3)b

But it's - 5ab in the middle, not + 5ab, so the answer is not ( (3/2)a + (5/3)b )^2.  The answer is ( (3/2)a - (5/3)b )^2