Question 512 Marks
Expand : $(a−b+c)^2$
AnswerNote : $(a+b+c)^2$
$= a^2 + b^2 + c^2 + 2ab − 2bc − 2ca(a−b+c)^2$
$= (a)^2 + (−b)^2 + (c)^2 + 2 \times a \times −b + 2(−b)(c) + 2\times c \times a$
$= a^2+ b^2+ c^2 − 2ab − 2bc + 2ca$
View full question & answer→Question 522 Marks
Expand: $\left(a+\frac{1}{2 a}\right)^2$
Answer$ \left(a+\frac{1}{2 a}\right)^2$
$=(a)^2+\left(\frac{1}{2 a}\right)^2+2 \times a \times \frac{1}{2 a}$
$ =a^2+\frac{1}{4 a^2}+\frac{2 a}{2 a}$
$ =a^2+\frac{1}{4 a^2}+1$
View full question & answer→Question 532 Marks
Evaluate : $(9a − 7b) (3a − b)$
Answer$(9a − 7b) (3a − b)$
$= 9a (3a − b) − 7b (3a − b)$
$= 27a^2 − 9ab − 21ab + 7b^2$
$= 27a^2 − 30ab + 7b^2$
View full question & answer→Question 542 Marks
Evaluate : $(2a − 3b) (3a + 4b)$
Answer$(2a − 3b) (3a + 4b)$
$= 2a (3a + 4b) − 3b (3a + 4b)$
$= 6a^2 + 8ab − 9ab − 12b^2$
$= 6a^2 − ab − 12b^2$
View full question & answer→Question 552 Marks
Evaluate : $(7x + 15y) (5x − 4y)$
Answer$(7x + 15y) (5x − 4y)$
$= 7x (5x − 4y) + 15y (5x − 4y)$
$= 35x^2 − 28xy + 75xy − 60y^2$
$= 35x^2 + 47xy − 60y^2$
View full question & answer→Question 562 Marks
Evaluate : $(5x + 8y) (3x + 5y)$
Answer$(5x + 8y) (3x + 5y)$
$= 5x (3x + 5y) + 8y (3x+ 5y)$
$= 15x^2 + 25xy + 24xy + 40y^2$
$= 15x^2 + 49xy + 40y^2$
View full question & answer→Question 572 Marks
Evaluate : $(a + bc) (a − bc) (a^2 + b^2c^2)$
Answer$(a + bc) (a − bc) (a^2 + b^2c^2)$
$= [(a)^2 − (bc)^2] (a^2 + b^2c^2) ...........[(a+b) (a−b) = a^2 − b^2]$
$= (a^2− b^2c^2) (a^2+ b^2c^2) ..........[ \because (a+b) (c−b) = a^2 − b^2]$
$= a^4 − b^4c^4$
View full question & answer→Question 582 Marks
Evaluate: $\left(3 \mathrm{x}-\frac{1}{2 \mathrm{y}}\right)\left(3 \mathrm{x}+\frac{1}{2 \mathrm{y}}\right)$
Answer$ \left(3 x-\frac{1}{2 y}\right)\left(3 x+\frac{1}{2 y}\right)$
$ =3 x\left(3 x+\frac{1}{2 y}\right)-\frac{1}{2 y}\left(3 x+\frac{1}{2 y}\right)$
$ =9 x^2+\frac{3 x}{2 y}-\frac{3 x}{2 y}-\frac{1}{4 y^2}$
$ =9 x^2-\frac{1}{4 y^2}$
View full question & answer→Question 592 Marks
Evaluate: $\left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$
Answer$ \left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$
$ =\frac{\mathrm{a}}{2 \mathrm{~b}}\left(\frac{\mathrm{a}}{2 \mathrm{~b}}+\frac{2 \mathrm{~b}}{\mathrm{a}}\right)+\frac{2 \mathrm{~b}}{\mathrm{a}}\left(\frac{\mathrm{a}}{2 \mathrm{~b}}-\frac{2 \mathrm{~b}}{\mathrm{a}}\right)$
$ =\frac{\mathrm{a}^2}{4 \mathrm{~b}^2}-1+1-\frac{4 \mathrm{~b}^2}{\mathrm{a}^2}$
$ =\frac{\mathrm{a}^2}{4 \mathrm{~b}^2}-\frac{4 \mathrm{~b}^2}{\mathrm{a}^2}$
View full question & answer→Question 602 Marks
Evaluate: $\left(7 x+\frac{2}{3} y\right)\left(7 x-\frac{2}{3} y\right)$
Answer$ \left(7 x+\frac{2}{3} y\right)\left(7 x-\frac{2}{3} y\right)$
$ =7 x\left(7 x-\frac{2}{3} y\right)+\frac{2}{3} y\left(7 x-\frac{2}{3} y\right)$
$ =49 x^2-\frac{14}{3} x y+\frac{14}{3} x y-\frac{4}{9} y$
$ =49 x^2-\frac{4}{9} y^2$
View full question & answer→Question 612 Marks
Use the product $(a + b) (a – b) = a^2 – b^2$ to evaluate: $4.6 \times 5.4$
Answer$4.6 \times 5.4$
$= (5−0.4) (5+0.4)$
$= (5)^2− (0.4)^2$
$= 25 − 0.16$
$= 24.84$
View full question & answer→Question 622 Marks
Use the product $(a + b) (a – b) = a^2 – b^2 $ to evaluate: $7.7 \times 8.3$
Answer$7.7 \times 8.3$
$= (8−0.3) (8+0.3)$
$= (8)^2− (0.3)^2$
$= 64 − 0.09$
$= 63.91$
View full question & answer→Question 632 Marks
Use the product $(a + b) (a – b) = a^2 – b^2$ to evaluate: $9.8 \times 10.2$
Answer$9.8 \times 10.2 = (10−0.2) (10+0.2)$
$= (10)^2 − (0.2)^2$
$= 100 − 0.04$
$= 99.96$
View full question & answer→Question 642 Marks
Use the product $(a + b) (a – b) = a^2 – b^2 $ to evaluate: $103 \times 97$
Answer$103 \times 97$
$= (100+3) (100−3)$
$= (100)^2 − (3)^2$
$= 10000 − 9$
$= 9991$
View full question & answer→Question 652 Marks
Use the product $(a + b) (a – b) = a^2 – b^2 $ to evaluate: $33 \times 27$
Answer$33 \times 27$
$= (30+3) (30−3)$
$= (30)^2 − (3)^2$
$= 900 − 9$
$= 891$
View full question & answer→Question 662 Marks
Use the product $(a + b) (a – b) = a^2 – b^2$ to evaluate: $21 \times 19$
Answer$21 \times 19$
$= (20+1) (20−1)$
$= (20)^2 − (1)^2$
$= 400 − 1$
$= 399$
View full question & answer→Question 672 Marks
Evaluate : $(3x−4y) (3x+4y) (9x^2+16y^2)$
Answer$(3x−4y) (3x+4y) (9x^2+16y^2)$
$= [(3x)^2−(4y)^2] (9x^2+16y^2)$
$= (9x^2−16y^2) (9x^2+16y^2)$
$= (9x^2)^2 − (16y^2)^2$
$= 81x^4 − 256y^4$
View full question & answer→Question 682 Marks
Evaluate :$(3−2x) (3+2x) (9+4x^2)$
Answer$(3−2x) (3+2x) (9+4x^2)$
$= [{3}^2−(2x)^2] (9+4x^2)$
$= (9−4x^2) (9+4x^2)$
$= (9)^2 − (4x^2)^2$
$= 81 − 16x^4$
View full question & answer→Question 692 Marks
Evaluate : $(2a−b) (2a+b) (4a^2+b^2)$
Answer$(2a−b) (2a+b) (4a^2+b^2)$
$= [(2a)^2−(b)^2] (4a^2+b^2)$
$= (4a^2−b^2) (4a^2+b^2)$
$= (4a^2)^2 − (b^2)^2$
$= 16a^4 − b^4$
View full question & answer→Question 702 Marks
Evaluate :$(a+b) (a−b) (a^2+b^2)$
Answer$(a+b) (a−b) (a^2+b^2)$
$= (a^2−b^2) (a^2+b^2)$
$= (a^2)^2− (b^2)^2$
$= a^4 − b^4$
View full question & answer→Question 712 Marks
Evaluate : $(a+1) (a-1) (a^2+1)$
Answer$(a+1) (a-1) (a^2+1)$
$= [(a)^2−(1)^2] (a^2+1)$
$= (a^2−1) (a^2+1)$
$= (a^2)^2 − (1)^2$
$= a^4 − 1$
View full question & answer→Question 722 Marks
Use the direct method to evaluate: $\left(\frac{3}{5} a+\frac{1}{2}\right)\left(\frac{3}{5} a-\frac{1}{2}\right)$
AnswerNote: $(a+b)(a-b)=a^2-b^2$
$\left(\frac{3}{5} a+\frac{1}{2}\right)\left(\frac{3}{5} a-\frac{1}{2}\right)$
$ =\left(\frac{3}{5} a\right)^2-\left(\frac{1}{2}\right)^2$
$ =\frac{9}{25} a^2-\frac{1}{4}$
View full question & answer→Question 732 Marks
Use the direct method to evaluate: $\left(\frac{\mathrm{a}}{2}-\frac{\mathrm{b}}{3}\right)\left(\frac{\mathrm{a}}{2}+\frac{\mathrm{b}}{3}\right)$
AnswerNote: $(a+b)(a-b)=a^2-b^2$
$\left(\frac{\mathrm{a}}{2}-\frac{\mathrm{b}}{3}\right)\left(\frac{\mathrm{a}}{2}+\frac{\mathrm{b}}{3}\right)$
$ =\left(\frac{\mathrm{a}}{2}\right)^2-\left(\frac{\mathrm{b}}{3}\right)^2$
$ =\frac{\mathrm{a}^2}{4}-\frac{\mathrm{b}^2}{9}$
View full question & answer→Question 742 Marks
Use the direct method to evaluate : $(0.5a−2a) (0.5+2a)$
AnswerNote: $(a+b) (a−b) $
$= a^2 − b^2(0.5a−2a) (0.5+2a)$
$= (0.5)^2 − (2a)^2$
$= 0.25 − 4a^2$
View full question & answer→Question 752 Marks
Use the direct method to evaluate: $\left(\mathrm{z}-\frac{2}{3}\right)\left(\mathrm{z}+\frac{2}{3}\right)$
AnswerNote: $(a+b)(a-b)=a^2-b^2$
$\left(z-\frac{2}{3}\right)\left(z+\frac{2}{3}\right)$
$=(z)^2-\left(\frac{2}{3}\right)^2$
$ =z^2-\frac{4}{9}$
View full question & answer→Question 762 Marks
Use the direct method to evaluate : $(4+5x) (4−5x)$
AnswerNote: $(a+b) (a−b)$
$= a^2 − b^2(4+5x) (4−5x)$
$= (4)^2 − (5x)^2$
$= 16 − 25x^2$
View full question & answer→Question 772 Marks
Use the direct method to evaluate : $(3b−1) (3b+1)$
AnswerNote: $(a+b) (a−b)$
$= a^2 − b^2(3b−1) (3b+1)$
$= (3b)^2− (1)^2$
$= 9b^2 − 1$
View full question & answer→Question 782 Marks
Use the direct method to evaluate the following products : $(5a + 16) (3a – 7)$
Answer$(5a + 16) (3a – 7)$
$= (5a \times 3a) + (5a \times −7) + (16 \times 3a) + 16 −7$
$= 15a^2 + (−35a) + 48a + (−112)$
$= 15a^2− 35a + 48a − 112$
$= 15a^2 + 13a − 112$
View full question & answer→Question 792 Marks
Use the direct method to evaluate the following products : $(y + 5)(y – 3)$
Answer$(y + 5) (y – 3)$
$= (y \times y) + (y \times −3) + (5 \times y) + (5 \times −3)$
$= y^2 + (−3y) + (5y) − 15$
$= y^2− 3y + 5y − 15$
$= y^2 + 2y − 15$
View full question & answer→Question 802 Marks
Use direct method to evaluate the following products : $(x + 8)(x + 3)$
Answer$(x + 8) (x + 3)$
$= (x \times x) + (x \times 3) + (8 \times x) + (8 \times 3)$
$= x^2 + 3x + 8x + 24$
$= x^2 + 11x + 24$
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