Question

Chapter
3
(ii) 6x2 - 12x
(ii) 21pq2r + 42pq2r3
(ii) 6x3 + 6x2 + 12x
(ii) 36a3b3c - 18ab2c2 + 27ab2c
(ii) (x + 3y)322 - (2x + 6y)z
(ii) 4x(x2 + y2) - 8(x2 + y2)
10. 20x(2a + b -c)3 + 15x2 (2a + b - c)2 – 5x3(2a + b -c)
(ii) 6(x - 2y)3 – 18(x – 2y)2
12. (2x + 3y) (2a - 3b) + (3x – 4y) (2a - 3b)
44. xy(x + 3y) - 4x?y(x + 3y)2 + 8xy-(x + 3y)3
3. (i) 9m + 18n
(4. (i) 15a2b-c-3abc2
5. (i) 583 + 10x2 + 15x
6. (i) 14p²q2 + 21pq - 28pq?
7. (i) 7X(3p + 49) - 14x2(3p + 49)
8. (i) 8r2(a2 + b2) + 12x(a2 +62)
9. (i) 4(x + 3y)3 + 12(x + 3y)2
11.) 5xy - 15x3y3 + 25x²,4 – 35xy5
13. 3y(x + 3y) + 3(x + 3y)2
Factorisation by Grouping
When an algebraic expression contains an even number of terms, then factorisation b
The given expression can be factorised by using the following steps:
Steps: (i) Arrange the terms of the given expression in groups, such that each grou
(ii) Factorise each group.
ator which is common to each group.​

Answer 1

Answer:

Simplify (4x2 – 4x – 7)(x + 3)

Here's what the multiplication looks like when it's done horizontally:

(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:

4x3 + 8x2 – 19x – 21