Question

(5-y)^2 (1+2d)^2 (8+5y)^2 (2+8c)^2 (4a+3)^2

Answer 1

1. 25-10у+у^2
2. 1+4d+4d^2
3. 64+80y+25y^2
4. 4+32c+64c^2
5. 16a^2+24a+9

Answer 2

To simplify this expression, we can expand each factor using the formula for the square of a binomial:

(5-y)^2 = 25 - 10y + y^2 (1+2d)^2 = 1 + 4d + 4d^2 (8+5y)^2 = 64 + 80y + 25y^2 (2+8c)^2 = 4 + 32c + 64c^2 (4a+3)^2 = 16a^2 + 24a + 9

Multiplying all these expansions together, we get:

(25 - 10y + y^2) * (1 + 4d + 4d^2) * (64 + 80y + 25y^2) * (4 + 32c + 64c^2) * (16a^2 + 24a + 9)

We can simplify this expression further by using the distributive property of multiplication to combine like terms. This results in:

1600 a^2 c^2 d^2 - 2880 a^2 c^2 d - 720 a^2 c^2 + 2880 a^2 cd^2 - 5184 a^2 cd + 1152 a^2 + 1440 acd^2 - 2592 acd + 576 ac + 1440 ad^2 - 2592 ad + 576 a + 625c^2 + 800yc^2 + 64c + 2000cd^2y - 3600cdy + 500d^2y^2 + 1000dy^2 - 100dy + 25y^4 - 50y^3 + 25y^2

Therefore, the simplified expression is:

1600 a^2 c^2 d^2 - 2880 a^2 c^2 d - 720 a^2 c^2 + 2880 a^2 cd^2 - 5184 a^2 cd + 1152 a^2 + 1440 acd^2 - 2592 acd + 576 ac + 1440 ad^2 - 2592 ad + 576 a + 625c^2 + 800yc^2 + 64c + 2000cd^2y - 3600cdy + 500d^2y^2 + 1000dy^2 - 100dy + 25y^4 - 50y^3 + 25y^2.