1. Factor completely each of the following: a. $4x^2y^2 - 6x^2y + 12xy^2$ d. $-16t^2 + 56t + 32$ b. $64m^2 - 16n^2$ e. $4x^2 + 21xy - 18y^2$ c. $x^2 + 5x - 24$ f. $28a^2 - ab - 2b^2$ 2*. Solve each of the following systems of equations by using addition: a. $2x - y = 2$ $x + 3y = 2$ c. $2x^2 - 3y^2 = 19$ $3x^2 + y^2 = 1$ b. $3x - 2y = 1$ $4x - 3y = 4$ 3*. Solve each of the following systems of equations by using substitution: a. $2x - y = 2$ $6x + 2y = 1$ c. $2x - y = 1$ $x - 3y = -2$ b. $2x - y = 2$ $xy = 4$ *You must show all work. You must check your answers.
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Step 1: To solve the system of equations by addition, we need to manipulate the equations so that when we add them together, one of the variables cancels out. Show more…
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(1) Factorise the following: (i) 6x^2 + 19x - 36 (ii) 6x^3 + 5x^2 - 22x - 24 (iii) 4x^3 - 36x^2 + 105x - 100 (2) Given that 2x^2 + 14x - 35 ≡ a(x + b)^2 + c, find the values of the constants a, b and c. (3) Solve x^2 + 2px - 16 = 0 by completing the square, giving your answers in terms of p. (4) Simplify the following expressions: (i) (9x^8 / 16)^(1/2) (ii) (64 / 27x^15)^(2/3) (5) Solve 27^(x+2) = 9^(2x-3) (6) The curve y = ax^2 + bx + c passes through the points (-4, 111), (2, 9) and (5, 39). By finding the values of the constants a, b and c, find the value of y when x = 7.
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Vadim M.
Factorize the following: (a) $36 x^{3} y^{2}-8 x^{2} y$ (e) $x^{2}+10 x+24$ (b) $x^{3}+3 x^{2} y+2 x y^{2}+6 y^{3}$ (f) $x^{2}-10 x+16$ (c) $4 x^{2}+12 x+9$ (g) $x^{2}-5 x-36$ (d) $(3 x+4 y)^{2}-(2 x-y)^{2}$ (h) $6 x^{2}+5 x-6$
Programme F.2 Introduction to algebra
Test exercise F.2
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