Question 1014 Marks
Find the square of $2x − 3y + z$
Answer$(2x − 3y + z)^2 $
$= (2x)^2 + (−3y)^2+ (z)^2 + 2 \times 2x \times −3y + 2(−3y) \times z + 2 \times z \times 2x= 4x^2 + 9y^2+ z^2− 12xy − 6yz + 4zx$
View full question & answer→Question 1024 Marks
Find the square of $5-x+\frac{2}{x}$
Answer$ \left(5-x+\frac{2}{x}\right)^2$
$=(5)^2+(-x)^2+\left(\frac{2}{x}\right)^2+2 \times 5 \times(-x)+2(-x) \times \frac{2}{x}+2 \times \frac{2}{x} \times 5$
$ =25+x^2+\frac{4}{x^2}-10 x-4+\frac{20}{x}$
$ =21+x^2+\frac{4}{x^2}-10 x+\frac{20}{x}$
View full question & answer→Question 1034 Marks
Find the square of $2 x+\frac{1}{x}+1$
Answer$ \left(2 \mathrm{x}+\frac{1}{\mathrm{x}}+1\right)^2$
$=(2 \mathrm{x})^2+\left(\frac{1}{\mathrm{x}}\right)^2+(1)^2+2 \times 2 \mathrm{x} \times \frac{1}{\mathrm{x}}+2 \times \frac{1}{\mathrm{x}} \times 1+2 \times 1 \times 2 \mathrm{x}$
$ =4 \mathrm{x}^2+\frac{1}{\mathrm{x}^2}+1+4+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
$ =4 \mathrm{x}+\frac{1}{\mathrm{x}^2}+5+\frac{2}{\mathrm{x}}+4 \mathrm{x}$
View full question & answer→Question 1044 Marks
Find the square of $3a − 2b − 5c$
Answer$(3a − 2b − 5c)^2 $
$= (3a)^2 + (−2b)^2+ (−5c)^2 + 2 \times 3a \times −2b + 2 \times (−2b)(−5c) + 2 \times −5c \times 3a$
$= 9a^2 + 4b^2 + 25c^2− 12ab + 20bc − 30ca$
View full question & answer→Question 1054 Marks
Find the square of $x − 2y +1$
Answer$(x − 2y +1)^2 $
$= (x)^2 + (−2y)^2+ (1)^2 + 2 \times x \times −2y + 2 \times (−2y) \times 1 + 2 \times 1 \times x$
$= x^2 + 4y^2 + 1 − 4xy − 4y + 2x$
View full question & answer→Question 1064 Marks
Find the square of $2 a-\frac{1}{a}$
Answer$ \left(2 \mathrm{a}-\frac{1}{\mathrm{a}}\right)^2$
$=(2 \mathrm{a})^2+\left(\frac{1}{\mathrm{a}}\right)^2-2 \times 2 \mathrm{a} \times \frac{1}{\mathrm{a}}$
$ =4 \mathrm{a}^2+\frac{1}{\mathrm{a}^2}-4$
View full question & answer→Question 1074 Marks
Find the square of $a+\frac{1}{5 a}$
Answer$ \left(\mathrm{a}+\frac{1}{5 \mathrm{a}}\right)^2$
$=(\mathrm{a})^2+\left(\frac{1}{5 \mathrm{a}}\right)^2+2 \times \mathrm{a} \times \frac{1}{5 \mathrm{a}}$
$ =\mathrm{a}^2+\frac{1}{25 \mathrm{a}^2}+\frac{2}{5}$
View full question & answer→Question 1084 Marks
Find the square of $2x − 5y$
Answer$(2x − 5y)^2 $
$= (2x)^2 + (5y)^2 − 2 \times 2x \times 5y$
$= 4x^2 + 25y^2 − 20xy$
View full question & answer→Question 1094 Marks
Find the square of $x+ 3y$
Answer$(x + 3y)^2$
$ = (x)^2 + (3y)^2+ 2\times x \times 3y$
$= x^2 + 9y^2+ 6xy$
View full question & answer→Question 1104 Marks
Expand: $\left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^2$
Answer$ \left(2 \mathrm{x}-\frac{1}{2 \mathrm{x}}\right)^2$
$=(2 \mathrm{x})^2+\left(\frac{1}{2 \mathrm{x}}\right)^2-2 \times 2 \mathrm{x} \times \frac{1}{2 \mathrm{x}}$
$ =4 \mathrm{x}^2+\frac{1}{4 \mathrm{x}^2}-2$
View full question & answer→Question 1114 Marks
Expand: $\left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)^2$
Answer$ \left(3 \mathrm{x}+\frac{1}{3 \mathrm{x}}\right)^2$
$=(3 \mathrm{x})^2+\left(\frac{1}{3 \mathrm{x}}\right)^2+2 \times 3 \mathrm{x} \times \frac{1}{3 \mathrm{x}}$
$ =9 \mathrm{x}^2+\frac{1}{9 \mathrm{x}^2}+2$
View full question & answer→Question 1124 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 1134 Marks
Expand : $(a+b−c)^2$
Answer$(a+b−c)^2 $
$= (a)^2 + (b)^2 +(−c)^2 + 2 \times a \times b + 2 \times b \times (−c) + 2 \times (−c) \times (a)$
$= a^2 + b^2 + c^2 + 2ab − 2bc − 2ca$
View full question & answer→Question 1144 Marks
Expand: $\left(2 a-\frac{1}{a}\right)^2$
Answer$ \left(2 \mathrm{a}-\frac{1}{\mathrm{a}}\right)^2$
$=(2 \mathrm{a})^2+\left(\frac{1}{\mathrm{a}}\right)^2-2 \times 2 \mathrm{a} \times \frac{1}{\mathrm{a}}$
$ =4 \mathrm{a}^2+\frac{1}{\mathrm{a}^2}-4$
View full question & answer→Question 1154 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 1164 Marks
Expand : $(a – 2b)^2$
Answer$(a – 2b)^2 $
$= (a)^2 + (2b)^2− 2 \times a \times 2b ........[(a−b)^2 = a^2 + b^2− 2ab]$
$= a^2+ 4b^2− 4ab$
View full question & answer→Question 1174 Marks
Expand : $(2a + b)^2$
Answer$(2a + b)^2$
$= (2a)^2 + (b)^2 + 2 \times 2a \times b ......[(a+b)^2 = a^2 + b^2+ 2ab]$
$= 4a^2 + b^2 + 4ab$
View full question & answer→Question 1184 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 1194 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 1204 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 1214 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 1224 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 1234 Marks
Evaluate : $(2a +3) (2a − 3) (4a^2 + 9)$
Answer$(2a +3) (2a − 3) (4a^2 + 9)$
$= [(2a)^2 − (3)^2] (4a^2 + 9) ..........[(a+b) (a−b) = a^2 − b^2]$
$= (4a^2 − 9) (4a^2 + 9)$
$= (4a^2)^2 − (9)^2 .........[(a+b) (a−b) = a^2 − b^2]$
$= 16a^4 − 81$
View full question & answer→Question 1244 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 1254 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 1264 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 1274 Marks
Evaluate : $(6 – xy) (6 + xy)$
Answer$(6-x y)(6+x y)$
$=6^2-(x y)^2$
$=36-x^2 y^2$
View full question & answer→Question 1284 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 1294 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 1304 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 1314 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 1324 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 1334 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 1344 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 1354 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 1364 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 1374 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 1384 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 1394 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 1404 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 1414 Marks
Use the direct method to evaluate : $(0.5a−2a) (0.5+2a)$
Answer$(a+b) (a−b) = a^2 − b^2(0.5a−2a) (0.5+2a)$
$= (0.5)^2 − (2a)^2$
$= 0.25 − 4a^2$
View full question & answer→Question 1424 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 1434 Marks
Use the direct method to evaluate : $(3x^2+5y^2) (3x^2−5y^2)$
Answer$(a+b) (a−b) $
$= a^2 − b^2(3x^2+5y^2) (3x^2−5y^2) $
$= (3x^2)^2 − (5y^2)^2$
$= 9x^4 − 25y^4$
View full question & answer→Question 1444 Marks
Use the direct method to evaluate : $(ab+x^2) (ab−x^2)$
Answer$(a+b) (a−b) $
$= a^2 − b^2(ab+x^2) (ab−x^2) $
$= (ab)^2 − (x^2)^2$
$= a^2b^2 − x^4$
View full question & answer→Question 1454 Marks
Use the direct method to evaluate : $(xy+4) (xy−4)$
Answer$(a+b) (a−b) $
$= a^2 − b^2(xy+4) (xy−4)$
$ = (xy)^2 − (4)^2$
$= x^2y^2 − 16$
View full question & answer→Question 1464 Marks
Use the direct method to evaluate : $(2a+3) (2a−3)$
AnswerNote : $(a+b) (a−b) $
$= a^2 − b^2(2a+3) (2a−3) $
$= (2a)^2 − (3)^2$
$= 4a^2− 9$
View full question & answer→Question 1474 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 1484 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 1494 Marks
Use the direct method to evaluate : $(2+a) (2−a)$
AnswerNote: $(a+b) (a−b)$
$= a^2 − b^2(2+a) (2−a)$
$= (2)^2 − (a)^2$
$= 4 − a^2$
View full question & answer→Question 1504 Marks
Use the direct method to evaluate : $(x+1) (x−1)$
AnswerNote: $(a+b) (a−b) .$
$= a^2 − b^2(x+1) (x−1)$
$= (x)^2 − (1)^2$
$= x^2− 1$
View full question & answer→