Question 1
Use a suitable identity to get each of the following products.
a) (p - 11) (p + 11)
b) (2y + 5) (2y - 5)
c) (12a - 9) (12a +9)
d) (2a-1/2)(2a-1/2)
e) (1.1m - 0.4) (1.1m + 0.4)
f) (a2+ b2) (- a2+ b2)
g) (6x - 7) (6x + 7)
h) (- a/2 + c/2) (- a/2 + c/2)
i) [(p/8)+(3q/4)] [(p/8)+(3q/4)]
j) (3a + 9b) (3a - 9b)
k) 2(a - 9)2
l) 5(xy - 3z)2
m) (6x+ 5y)2
n) 36[(3p/2}) + (2q/3)]2
o) (x - 0.5y)2
p) (2xy - 5y)2
Question 2
Use the identity (x + a) (x + b) = x2 + (a + b) x + ab to find the following products.
(i) (p + 10) (p + 11)
(ii) (4x + 9) (4x + 12)
(iii) (x - 5) (x - 1)
(iv) (9x - 5) (9x - 1)
(v) (2x + 5y) (2x + 3y)
(vi) (2a2+ 9) (2a2+ 5)
Answers
Answer:
Step-by-step explanation:
Identity (a-b)(a+b) = (a +b)(a-b) = a² - b²
a) (p - 11) (p + 11) = p² - 121
b) (2y + 5) (2y - 5) = 4y² - 25
c) (12a - 9) (12a +9) = 144a² - 81
e) (1.1m - 0.4) (1.1m + 0.4) = 1.21m² - 0.16
f) (a2+ b2) (- a2+ b2) = a⁴ - b⁴
g) (6x - 7) (6x + 7) = 36x² - 49
j) (3a + 9b) (3a - 9b) = 9a² - 81b²
(a-b)² = a² -2ab + b² (a+b)² = a² + 2ab + b²
d) (2a-1/2)(2a-1/2) = 4a² -a + 1/4
h) (- a/2 + c/2) (- a/2 + c/2) = a²/4 -ac/2 + c²/2
i) [(p/8)+(3q/4)] [(p/8)+(3q/4)] = p²/64 +3pq/16 + 9q²/16
k) 2(a - 9)² = 2(a² -18a + 81)
l) 5(xy - 3z)² = 5(x²y² - 6xyz + 9z²)
m) (6x + 5y)² = 36x² +60xy + 25y²
Use the identity (x + a) (x + b) = x² + (a + b) x + ab
(i) (p + 10) (p + 11) = p² + 21p + 110
(ii) (4x + 9) (4x + 12) = 16x² + 84x + 108
(iii) (x - 5) (x - 1) = x² -6x + 5
(iv) (9x - 5) (9x - 1) = 81x² -54x + 5
(v) (2x + 5y) (2x + 3y) = 4x² + 16xy + 15y²
(vi) (2a²+ 9) (2a²+ 5) = 4a⁴ + 28a² + 45
Answer:
We will be using below identities in these question
(a + b)² = a² + 2ab + b²
(a � b)² = a² � 2ab + b²
(a � b)(a + b) = a² � b²
(a) p² -121
(b) 4y² -25
(c) 144a²-81
(d) 4a²+1/4 -2a
(e) 1.21m² -.16
(f) b&sup4; -a&sup4;
(g) 36x² -49
(h) c²/4 - a²/4
(i) p²/64 + 9q²/16 +3pq/16 = (p²+36q²+12pq)/64
(j) 9a²-81b²
(k) 4(a² + 81-18a)
(l) 25(x²y²+9z²-6xyz)
(m) 36x²+25y²+60xy
(n) 36[9p²/4 + 4q²/9 + 2pq]= 9p²+16q² + 64pq
(o) x²+.25y²-xy
(p) 4x²y²+25y²-20xy²