Write (x-2)(x+4)=10 in the form ax^2 + bx + c = 0 and work out the values of a, b and c
We should begin by multiplying out the brackets. Firstly, multiply each term in the first bracket with the first term in the second bracket: x times x equals x2 and -2 multiplied by x is equal to -2x. Next, we multiply each term in the first bracket with the second term in the second bracket: x multiplied by 4 gives us 4x and -2 times 4 is equal to -8. We thus have 4 terms and can use them instead of the brackets in our equation, leaving us with x2 - 2x + 4x - 8 = 10.
We must take note, however, that the question asks for a specific form; 3 terms equaling 0. We must therefore simplify. We know that -2x + 4x = 2x and we thus have x2 + 2x - 8 = 10. The question requires that the equation equal 0, so we take away 10 from both sides: -8 -10 = -18. We are left with x2 + 2x - 18 = 0.
Finally, we must state what a, b and c are: a = 1, b = 2 and c = - 18.
