Algebraic factorization of 30a3b2 = 30 x a x a x a x b x b
For every 2 moles of A3, 3 moles of B2 react to form 6 moles of AB. Since we have 10 moles of A3, we need to double the moles of B2 reacting, which would be 15 moles of B2 to fully react with the 10 moles of A3. This would produce 30 moles of AB.
From the balanced equation, 2 moles of A3 react with 3 moles of B2 to produce 6 moles of AB. Therefore, if 10 moles of A3 are reacted, the ratio of moles of AB produced would be (10 moles A3 / 2 moles A3) * 6 moles AB = 30 moles AB.
a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2
a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
a3 - b3 = (a - b)(a2 + ab + b2) a3 + b3 = (a + b)(a2 - ab + b2)
0
(b2 - 20c2)(b2 + 4c2)
Sum and difference of two cubes is factored this way : a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
(a+b)3=a3+b3+3ab(a+b) a3+b3=(a+b)3-3ab(a+b) a3+b3=(a+b)(a2-ab+b2)
let binomial be (a + b)now (a+b)3 will be (a+b)(a+b)2 = (a+b)(a2 + 2ab+ b2) = a(a2+ 2ab+ b2) + b(a2 + 2ab+ b2) = a3+ 2a2b+ ab2 + a2b + 2ab2 + b3 = a3+ 2a2b+ ab2 + a2b + 2ab2 + b3 = a3 +3a2b + 3ab2 +b3 hope it helped... :D
a3+ b3 = (a + b)(a2 - ab + b2)