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1. Simplify (a+b)² - (a+b)(a-b).
2. Find the complete factorization of 3x rise to 4 - 48.
3. Find the product of (4a-5b)(16a² + 20ab + 25b²)
4. What value of "c" makes 25x²-30xy+c a perfect square trinomial?
5. The area of a square is (25a²x²-30axy+9y²) square units. How long is its side?

Sagot :

AnneCidn
1.
[tex](a+b)^2 - (a+b)(a-b) \\ \implies (a^2+2ab+b^2)-(a^2-b^2) \\ \implies a^2+2ab+b^2 -a^2+b^2 \\ \implies \boxed{2ab + 2b^2}[/tex]

2.
[tex]3x^4-48 \\ \implies 3(x^4-16)\\ \implies3(x^2+4)(x^2-4)\\ \implies\boxed{3(x^2+4)(x+2)(x-2)}[/tex]

3. (factor of difference of two cubes)
[tex](4a-5b)(16a^2 + 20ab + 25b^2)=\boxed{64a^3-125b^2}[/tex]

4. (b²-4ac=0) b=-30y ; a=25
  [tex](-30y)^2-4(25)c=0 \\ 900y^2-100c=0 \\ 900y^2=100c \\ \boxed{c=9y^2}[/tex]

5.
[tex]25a^2x^2-30axy+9y^2= (5ax-3y)^2 [/tex]
Its side measure [tex]\boxed{5ax-3y}[/tex]