Question 13 Marks
Factorise: $a^4 - 625$
Answer$a^4 - 625$
$= (a^2)^2 - (25)^2$
$= (a^2 + 25) (a^2 - 25) ....[a^2 - b^2 = (a + b)(a - b)]$
$= (a^2 + 25) \{(a)^2 - (5)^2\}$
$= (a^2 + 25) (a + 5)(a - 5)$
View full question & answer→Question 23 Marks
Factorise: $a^2 - 0·36\ b^2$
Answer$a^2 - 0·36\ b^2$
$= (a)^2 - (0.6b)^2$
$= (a + 0.6b)(a - 0.6b) ...[a^2 - b^2 = (a + b)(a - b)]$
View full question & answer→Question 33 Marks
Factorise: $25(a - 5b)^2 - 4(a - 3b)^2$
Answer$25(a - 5b)^2 - 4(a - 3b)^2$
$= [5 (a - 5b)]^2 - [2(a - 3b)]^2$
$= (5a - 25b)^2 - (2a - 6b)^2$
$= (5a - 25b + 2a - 6b)(5a - 25b - 2a + 6b)$
$.....[a^2 - b^2 = (a + b)(a - b)]$
$= (7a - 31b)(3a - 19b)$
View full question & answer→Question 43 Marks
Factorise: $(a - 3b)^2 - 36 b^2$
Answer$(a - 3b)^2 - 36 b^2$
$= (a - 3b)^2 - (6b)^2$
$= (a - 3b + 6b) (a - 3b - 6b)$
$= (a + 3b)(a - 9b) ....[a^2 - b^2 = (a + b)(a - b)]$
View full question & answer→Question 53 Marks
Factorise $xy^2 - xz^2,$ Hence, find the value of : $40 \times 5.5^2 - 40 \times 4.5^2$
Answer$xy^2 - xz^2$
$ = x(y^2 - z^2) $
$= x(y - z)(y + z)40 \times 5.5^2 - 40 \times 4.5^2$
$= 40 (5.5)^2 - (4.5)^2$
$= 40 (5.5 - 4.5) (5.5 + 4.5)$
$= 40 (1) (10) = 400$
View full question & answer→Question 63 Marks
Factorise $xy^2 - xz^2,$ Hence, find the value of : $9 \times 8^2 - 9 \times 2^2$
Answer$xy^2 - xz^2 $
$= x(y^2 - z^2)$
$ = x(y - z)(y + z)9 \times 8^2 - 9 \times 2^2$
$= 9 (8^2 - 2^2)$
$= 9(8 - 2)(8 + 2)$
$= 9 (6) (10) = 540$
View full question & answer→Question 73 Marks
factorise: $7a^5 - 567a$
Answer$7a^5 - 567a$
$= 7a(a^4 - 81)$
$= 7a (a^2)^2 - (9)^2$
$= 7a (a^2 + 9) (a^2 - 9)$
$= 7a (a^2 + 9) ((a)^2 - (3)^2)$
$= 7a (a^2 + 9) (a + 3)(a - 3)$
View full question & answer→Question 83 Marks
Factorise: $x^2 - y^2 - 2yz - z^2$
Answer$x^2 - y^2 - 2yz - z^2$
$= x^2 - (y^2 + 2yz + z^2)$
$= x^2 - (y + z)^2$
$= (x + y + z) \{x - (y + z)\}$
$= (x + y + z) (x - y - z)$
View full question & answer→Question 93 Marks
factorise: $1 - 3x - 3y - 4(x + y)^2$
Answer$1 - 3x - 3y - 4(x + y)^2$
$= 1 - 3(x + y) - 4(x + y)^2$
$= 1 - 4(x + y) + (x + y) - 4(x + y)^2$
$= 1[1 - 4(x + y)] + (x + y)[1 - 4(x + y)]$
$= [1 - 4x - 4y](1 + x + y)$
View full question & answer→Question 103 Marks
factorise: $ax^2 + b^2y - ab^2 - x^2y$
Answer$ax^2 + b^2y - ab^2 - x^2y$
$= ax^2 - ab^2 + b^2y - x^2y$
$= a(x^2 - b^2) + y(b^2 - x^2)$
$= a(x^2 - b^2) - y(x^2 - b^2)$
$= (x^2 - b^2)(a - y)$
$= (x - b)(x + b)(a - y)$
View full question & answer→Question 113 Marks
factorise: $b(c - d)^2 + a(d - c) + 3(c - d)$
Answer$b(c - d)^2 + a(d - c) + 3(c - d)$
$= b (c - d)^2 - a(c - d) + 3(c - d)$
$= (c - d) [b (c - d) - a + 3]$
$= (c - d) (bc - bd - a + 3)$
View full question & answer→Question 123 Marks
factorise: $15(5x - 4)^2 - 10(5x - 4)$
Answer$15(5x - 4)^2 - 10(5x - 4)$
$= 5(5x - 4) [3(5x - 4) - 2]$
$= 5 (5x - 4) (15x - 12 - 2)$
$= 5 (5x - 4) (15x - 14)$
View full question & answer→Question 133 Marks
factorise: $12(a + b)^2 - (a+ b) - 35$
Answer$12(a + b)^2 - (a+ b) - 35$
$= 12 (a + b)^2 - 21 (a + b) + 20 (a + b) - 7$
$= 3(a + b) [4 (a + b) - 7] + 5[4 (a + b) - 7]$
$= (4a + 4b - 7)(3a + 3b + 5)$
View full question & answer→Question 143 Marks
factorise: $(3x - 2y)^2 - 5(3x - 2y) - 24$
Answer$(3x - 2y)^2 - 5(3x - 2y) - 24$
$= (3x - 2y)^2 - 8(3x - 2y) + 3(3x - 2y) - 24$
$= (3x - 2y) (3x - 2y - 8) + 3 (3x - 2y - 8)$
$= (3x - 2y - 8)(3x - 2y + 3)$
View full question & answer→Question 153 Marks
factorise: $5 - 4x(1 + 3x)$
Answer$5 - 4x(1 + 3x)$
$= 5 - 4x - 12x^2$
$= 5 - 10x + 6x - 12x^2$
$= 5(1 - 2x)+ 6x (1 - 2x)$
$= (1 - 2x)(5 + 6x)$
View full question & answer→Question 163 Marks
factorise: $x(3x + 14) + 8$
Answer$x(3x + 14) + 8$
$= 3x^2 + 14x + 8$
$= 3x^2 + 12x +2x +8$
$= 3x(x + 4) + 2(x + 4)$
$= (x + 4)(3x + 2)$
View full question & answer→Question 173 Marks
factorise: $5x^2 - 4xy - 12y^2$
Answer$5x^2 - 4xy - 12y^{2}$
$= 5x^2 - 10xy + 6xy - 12y^2$
$= 5x (x - 2y) + 6y (x - 2y)$
$= (x - 2y)(5x + 6y)$
View full question & answer→Question 183 Marks
factorise: $1 - 18x - 63x^2$
Answer$1 - 18x - 63x^2$
$= 1 - 21x + 3x - 63x^2$
$= 1 (1 - 21x) + 3x (1 - 21x)$
$= (1 - 21 x) (1 + 3x)$
View full question & answer→Question 193 Marks
factorise: $a^2 - 23a -108$
Answer$a^2 - 23a -108$
$= a^2 - 27a + 4a - 108 ...[27 \times 4 = 108$ and $27 -4 = 23]$
$= a(a - 27) + 4(a - 27)$
$= (a - 27)(a + 4)$
View full question & answer→Question 203 Marks
factorise: $a^2 - 23a + 42$
Answer$a^2 - 23a + 42 ...[42 = 21 \times 2$ and $21 + 2 = 23]$
$= a^2 - 21a - 2a + 42$
$= a(a - 21) - 2(a - 21)$
$= (a - 21)(a - 2)$
View full question & answer→Question 213 Marks
factorise: $25(x - 2y)^2 - 4$
Answer$25(x - 2y)^2 - 4$
$= (5(x - 2y))^2 - 2^2$
$= [5 (x - 2y) - 2] [5 (x - 2y) + 2] ...[a^2 - b^2 = (a - b)(a + b)]$
$= (5x - 10y - 2)(5x - 10y + 2)$
View full question & answer→Question 223 Marks
factorise : $25(2x - y)^2 - 16(x - 2y)^2$
Answer$25(2x - y)^2 - 16(x - 2y)^2= (5 (2x - y))^2 - (4 (x - 2y))^2$
$= [5(2x - y) - 4 (x - 2y)][5(2x - y) + 4(x - 2y)]$
$= [10x - 5y - 4x + 8y][10x - 5y + 4x - 8y]$
$....[a^2 - b^2 = (a - b)(a + b)]$
$= (6x + 3y)(14x - 13y)$
$= 3(2x + y)(14x - 13y)$
View full question & answer→Question 233 Marks
factorise : $m - 1 - (m-1)^2 + am - a$
Answer$m - 1 - (m-1)^2 + am - a$
$= (m - 1) - (m - 1)^2 + a (m - 1)$
$= (m - 1) (1 - (m - 1) + a)$
$= (m - 1) (1 - m + 1 + a)$
$= (m - 1) (2 - m + a)$
View full question & answer→Question 243 Marks
factorise : $ab(x^2 + y^2) - xy (a^2 + b^2)$
Answer$ab(x^2 + y^2) - xy (a^2 + b^2)$
$= abx^2 + aby^2 - a^2xy - b^2xy$
$= abx^2 - a^2xy + aby^2 - b^2xy$
$= abx^2 - a^2xy - b^2xy + aby^2$
$= ax (bx - ay) - by (bx - ay)$
$= (bx - ay)(ax - by)$
View full question & answer→Question 253 Marks
Evaluate $($using factors$)$ : $301^2 \times 300 - 300^3.$
Answer$301^2 \times 300 - 300^3$
$= 300 (301^2 - 300^2)$
$= 300 (301 + 300)(301 - 300)$
$= 300 (601)(1)$
$= 180300$
View full question & answer→Question 263 Marks
Factorise completely: $625 - x^4$
Answer$625 - x^4 $
$= (25)^2 - (x^2)^2$
$= (25 + x^2) (25 - x^2)$
$= (25 + x^2) [(5)^2 - (x)^2]$
$= (25 + x^2) (5 + x) (5 - x)$
View full question & answer→Question 273 Marks
Factorise completely: $16x^4 - 81y^4$
Answer$16x^4 - 81y^4 $
$= (4x^2)^2 - (9y^2)^2$
$= (4x^2 + 9y^2) (4x^2 - 9y^2)$
$= (4x^2 + 9y^2)[(2x)^2 - (3y)^2]$
$= (4x^2 + 9y^2)(2x + 3y)(2x - 3y)$
View full question & answer→Question 283 Marks
Factorise completely: $a^2 - 16b^2 - 2a - 8b$
Answer$a^2 - 16b^2 - 2a - 8b$
$= (a)^2 - (4b)^2 - 2(a + 4b)$
$= (a + 4b)(a - 4b) - 2(a + 4b)$
$= (a + 4b)(a - 4b - 2)$
View full question & answer→Question 293 Marks
Factorise completely: $4a^2 -12ab + 9b^2 + 4a- 6b$
Answer$4a^2 -12ab + 9b^2 + 4a- 6b$
$= [(2a)^2 - 2 \times 2a \times 3b + (3b)^2] + 2(2a - 3b)$
$= (2a - 3b)^2 + 2(2a - 3b)$
$= (2a - 3b)(2a - 3b + 2)$
View full question & answer→Question 303 Marks
Factorise completely: $x^2 + 6xy + 9y^2 + x + 3y$
Answer$x^2 + 6xy + 9y^2 + x + 3y$
$= [(x)^2 + 2 \times x \times 3y + (3y)^2] + (x + 3y)$
$= [x + 3y]^2 + (x + 3y)$
$= (x + 3y) (x + 3y) + (x + 3y)$
$= (x + 3y) (x + 3y + 1)$
View full question & answer→Question 313 Marks
Factorise completely: $5ap^2 + 11ap + 2a$
Answer$5ap^2 + 11ap + 2a$
$= a[5p^2 + 11p + 2]$
$= a[5p^2 + 10p + p +2]$
$= a[5p(p+2) + 1(p + 2)]$
$= a[(p + 2)(5p + 1)]$
$= a (p + 2) (5p + 1)$
View full question & answer→Question 323 Marks
In the case find whether the trinomial is a perfect square or not: $16x^2 - 16xy + y^2$
Answer$16x^2 - 16xy + y^2$
$= (4x)^2 - 4 \times 4x \times y + (y)^2$
$= a^2 - 4ab + b^2$
$...[$Taking $4x = a,$ and $y = b]$
$∴$ The given trinomial cannot be expressed as $a^2 + 2ab + b^2 .$
Hence, it is not a perfect square.
View full question & answer→Question 333 Marks
Factorise completely: $3x^2y + 11xy + 6y$
Answer$3x^2y + 11xy + 6y$
$= y(3x^2 + 11x + 6)$
$= y[(3x^2 + 9x + 2x + 6)]$
$= y[3x (x + 3) + 2(x + 3)]$
$= y [(x + 3)(3x + 2)]$
$= y (x + 3)(3x + 2)$
View full question & answer→Question 343 Marks
Factorise completely: $5b^2 + 45b + 90$
Answer$5b^2 + 45b + 90$
$ = 5[b^2 + 9b + 18]$
$= 5[b^2 + 6b + 3b + 18]$
$= 5[b(b + 6) + 3(b + 6)]$
$= 5[(b + 6) (b + 3)]$
$= 5 (b + 6)(b + 3)$
View full question & answer→Question 353 Marks
Factorise completely: $2a^2 - 8a - 64$
Answer$2a^2 - 8a - 64$
$= 2[a^2 - 4a - 32]$
$= 2[a^2 - 8a + 4a - 32]$
$= 2[a(a - 8) + 4(a - 8)]$
$= 2[(a - 8) (a + 4)]$
$= 2(a - 8)(a + 4)$
View full question & answer→Question 363 Marks
Factorise completely: $3x^2 + 15x - 72$
Answer$3x^2 + 15x - 72$
$= 3 (x^2 + 5x - 24)$
$= 3[x^2 + 8x - 3x - 24]$
$= 3[x (x + 8) - 3 (x + 8)]$
$= 3[(x + 8)(x - 3)]$
$= 3 (x + 8)(x - 3)$
View full question & answer→Question 373 Marks
factorise: $x^2 - 10xy + 24y^2$
Answer$x^2 - 10xy + 24y^2$
$= x^2 - 6xy - 4xy + 24y^2$
$= x(x - 6y) - 4y(x - 6y)$
$= (x - 6y) (x - 4y)$
View full question & answer→Question 383 Marks
factorise: $x^2 - x - 72$
Answer$x^2 - x - 72$
$= x2 - 9x + 8x - 72$
$= x(x - 9) + 8(x - 9)$
$= (x - 9)(x + 8)$
View full question & answer→Question 393 Marks
factorise: $a^2 - 3a- 40$
Answer$a^2 - 3a- 40$
$= a^2 - 8a + 5a - 40$
$= a(a - 8) + 5(a - 8)$
$= (a - 8)(a + 5)$
View full question & answer→Question 403 Marks
factorise: $x^2 + 5xy + 4y^2$
Answer$x^2 + 5xy + 4y^2$
$= x^2 + 4xy + xy + 4y^2$
$= x(x + 4y) + y (x + 4y)$
$= (x + 4y)(x + y)$
View full question & answer→Question 413 Marks
factorise: $a^2 +5a - 6$
Answer$a^2 +5a - 6$
$= a2 + 6a - a - 6$
$= a (a + 6) - 1 (a + 6)$
$= (a + 6) (a - 1)$
View full question & answer→Question 423 Marks
factorise: $5 + 3a - 14a^2$
Answer$5 + 3a - 14a^25 + 10a - 7a - 14a^2$
$= 5(1 + 2a) - 7a (1 + 2a)$
$= (1 + 2a) (5 - 7a)$
View full question & answer→Question 433 Marks
factorise: $4 + y - 14y^2$
Answer$4 + y - 14y^2$
$= 4 + 8y - 7y - 14y^2$
$= 4 (1 + 2y) - 7y (1 + 2y)$
$= (1 + 2y)(4 - 7y)$
View full question & answer→Question 443 Marks
factorise: $5 + 7x - 6x^2$
Answer$5 + 7x - 6x^2$
$= 5 + 10x - 3x - 6x^2$
$= 5(1 + 2x) - 3x(1 + 2x)$
$= (1 + 2x)(5 - 3x)$
View full question & answer→Question 453 Marks
factorise: $6 + 7b - 3b^2$
Answer$6 + 7b - 3b^2$
$= 6 + 9b - 2b - 3b^2$
$= 3(2 + 3b) - b(2 + 3b)$
$= (2 + 3b)(3 - b)$
View full question & answer→Question 463 Marks
factorise: $14x^2 + x - 3$
Answer$14x^2 + x - 3$
$= 14x^2 + 7x - 6x - 3$
$= 7x (2x + 1) - 3(2x + 1)$
$= (2x + 1) (7x - 3)$
View full question & answer→Question 473 Marks
factorise: $4c^2 + 3c - 10$
Answer$4c^2 + 3c - 10$
$= 4c^2 + 8c - 5c - 10$
$= 4c (c + 2) - 5(c + 2)$
$= (c + 2)(4c - 5)$
View full question & answer→Question 483 Marks
factorise: $2x^2 + xy - 6y^2$
Answer$2x^2 + xy - 6y^2$
$= 2x^2 + 4xy - 3xy - 6y^2$
$= 2x (x + 2y) - 3y(x + 2y)$
$= (x + 2y)(2x - 3y)$
View full question & answer→Question 493 Marks
factorise: $2a^2 - 17ab + 26b^2$
Answer$2a^2 - 17ab + 26b^2$
$= 2a^2 - 13ab - 4ab + 26b^2$
$= a(2a - 13b) - 2b(2a - 13b)$
$= (2a - 13b) (a - 2b)$
View full question & answer→Question 503 Marks
Factorise: $7b^2 - 8b + 1$
Answer$7b^2 - 8b + 1$
$= 7b^2 - 7b - b +1$
$= 7b(b - 1) - 1(b - 1)$
$= (7b - 1)(b - 1)$
View full question & answer→