Simplify and factorize the following algebraic expressions: -9x(x2 - 3) - 5x(2x2 - 5), 3(2a - 7)2, (3x - 3)(2x + 2), and -3t2 - 15.

Here are the solutions to your math questions. QUESTION 1 1.1 Simplify the following 1.1.1 -9x(x^2 - 3) - 5x(2x^2 - 5) Step 1: Distribute -9x into the first parenthesis and -5x into the second parenthesis. = -9x · x^2 - 9x · (-3) - 5x · 2x^2 - 5x · (-5) = -9x^3 + 27x - 10x^3 + 25x Step 2: Combine like terms. = (-9x^3 - 10x^3) + (27x + 25x) = -19x^3 + 52x The simplified expression is -19x^3 + 52x. 1.1.2 3(2a - 7)^2 Step 1: Expand the squared term (2a - 7)^2 using the formula (A-B)^2 = A^2 - 2AB + B^2. (2a - 7)^2 = (2a)^2 - 2(2a)(7) + (7)^2 = 4a^2 - 28a + 49 Step 2: Multiply the result by 3. = 3(4a^2 - 28a + 49) = 3 · 4a^2 - 3 · 28a + 3 · 49 = 12a^2 - 84a + 147 The simplified expression is 12a^2 - 84a + 147. 1.1.3 (3x - 3)(2x + 2) Step 1: Use the FOIL method (First, Outer, Inner, Last) or distributive property to multiply the binomials. = (3x)(2x) + (3x)(2) + (-3)(2x) + (-3)(2) = 6x^2 + 6x - 6x - 6 Step 2: Combine like terms. = 6x^2 + (6x - 6x) - 6 = 6x^2 - 6 The simplified expression is 6x^2 - 6. 1.2 Factorise the following 1.2.1 -3t^2 - 15 Step 1: Find the greatest common factor (GCF) of -3t^2 and -15. The GCF is -3. Step 2: Factor out the GCF. = -3(t^2 + 5) The factorised expression is -3(t^2 + 5). 1.2.2 5x(2x + 1) - 5(2x + 1) Step 1: Identify the common binomial factor, which is (2x + 1). Step 2: Factor out the common binomial. = (2x + 1)(5x - 5) Step 3: Notice that 5x - 5 has a common factor of 5. = 5(2x + 1)(x - 1) The factorised expression is 5(2x + 1)(x - 1). 1.2.3 2x(y - p) - 5d(2x + 1) This expression does not have a common factor between the two terms 2x(y-p) and 5d(2x+1). Therefore, it cannot be factored further in a simple way. The expression is 2x(y - p) - 5d(2x + 1). 1.2.4 81 - y^2 Step 1: Recognize this as a difference of squares, A^2 - B^2 = (A - B)(A + B), where A = sqrt(81) = 9 and B = sqrt(y^2) = y. = (9 - y)(9 + y) The factorised expression is (9 - y)(9 + y). QUESTION 2 2.1 Simplify the following 2.1.1 (10x^4 + 15x^2)/(-5x) Step 1: Divide each term in the numerator by the denominator. = (10x^4)/(-5x) + (15x^2)/(-5x) Step 2: Simplify each term. = -2x^4-1 - 3x^2-1 = -2x^3 - 3x The simplified expression is -2x^3 - 3x. 2.1.2 (3xy + y^2)/(x - 2) Step 1: Factor out the common factor y from the numerator. = (y(3x + y))/(x - 2) There are no common factors between the numerator and the denominator to cancel. The simplified expression is (y(3x + y))/(x - 2). 2.1.3 (x^2 + 2x - 8)/(x - 2) Step 1: Factor the quadratic expression in the numerator x^2 + 2x - 8. We need two numbers that multiply to -8 and add to 2. These numbers are 4 and -2. x^2 + 2x - 8 = (x + 4)(x - 2) Step 2: Substitute the factored numerator back into the expression. = ((x + 4)(x - 2))/(x - 2) Step 3: Cancel the common factor (x - 2), assuming x ≠ 2. = x + 4 The simplified expression is x + 4. 2.2 Solve for x 2.2.1 x - 19 = 14 Step 1: Add 19 to both sides of the equation. x - 19 + 19 = 14 + 19 x = 33 The solution is x = 33. 2.2.2 3x - 10 = -22 Step 1: Add 10 to both sides of the equation. 3x - 10 + 10 = -22 + 10 3x = -12 Step 2: Divide both sides by 3. (3x)/(3) = (-12)/(3) x = -4 The solution is x = -4. 2.2.3 x^2 + 9x = -14 Step 1: Move all terms to one side to set the equation to zero. x^2 + 9x + 14 = 0 Step 2: Factor the quadratic expression. We need two numbers that multiply to 14 and add to 9. These numbers are 2 and 7. (x + 2)(x + 7) = 0 Step 3: Set each factor equal to zero and solve for x. x + 2 = 0 or x + 7 = 0 x = -2 or x = -7 The solutions are x = -2 or x = -7. QUESTION 3 3.1 Say whether the following graphs are (increasing, decreasing or constant) 3.1.1 The graph shows a line sloping downwards from left to right. This graph is decreasing. 3.1.2 The graph shows a line sloping upwards from left to right. This graph is increasing. 3.1.3 The graph shows a horizontal line. This graph is constant. 3 done, 2 left today. You're making progress.