Question

(b) Find the products.
() (x2 - 4x + 5) (x + 3)
(ii) ( 5x2 + 3x + 7) (2x - 3)​

Answer 1

Step-by-step explanation:

4x2 – 4x – 7)(x + 3)

(4x2 – 4x – 7)(x) + (4x2 – 4x – 7)(3)

4x2(x) – 4x(x) – 7(x) + 4x2(3) – 4x(3) – 7(3)

4x3 – 4x2 – 7x + 12x2 – 12x – 21

4x3 – 4x2 + 12x2 – 7x – 12x – 21

4x3 + 8x2 – 19x – 21

That was painful! Now I'll do it vertically:

4x^2 – 4x – 7 is positioned above x + 3; first row: +3 times –7 is –21, carried down below the +3; +3 times –4x is –12x, carried down below the x; +3 times 4x^2 is +12x^2, carried down to the left of the –12x; second row: x times –7 is –7x, carried down below the –12x; x times –4x is –4x^2, carried down below the +12x^2; x times 4x^2 is 4x^3, carried down to the left of the –4x^2; adding down: 4x^3 + (+12x^2) + (–4x^2) + (–12x) + (–7x) + (–21) = 4x^3 + 8x^2 – 19x – 21

That was a lot easier! But, by either method, the answer is the same:

Answer 2

Answer:

b)

i) (x² - 4x + 5) (x + 3)

= x³ - 4x² + 5x + 3x² - 12x + 15

= x³ + ( -4x² + 3x²) + (5x -12x) + 15

= x³ + (-x²) + (-7x) + 15

= x³ - x² - 7x + 15

ii) (5x² + 3x + 7) (2x - 3)

= 10x³ + 6x² + 14x - 15x² - 9x - 21

= 10x³ + (6x² - 15x²) + ( 14x - 9x) - 21

= 10x³ + (-9x²) + (5x) -21

= 10x³ - 9x² + 5x - 21

Hope it helped you....