Question

write 25 expanison formulas and proov 15 of them​

Answer 1

Answer:

Question 1:

Expand.

(i) ( 5a + 6b)2 (ii) (a2 + b3)2 (iii) (2p − 3q)2 (iv) (x − 2x)2

(v) (ax + by)2 (vi) (7m − 4)2 (vii) (x +12)2 (viii) (a − 1a)2

ANSWER:

It is known that, (a + b)2 = a2 + 2ab + b2 and (a − b)2 = a2 − 2ab + b2.

(i) (5a+6b)2=(5a)2+2×(5a)(6b)+(6b)2=25a2+60ab+36b2

(ii) (a2+b3)2=(a2)2+2×(a2)×(b3)+(b3)2=a24+ab3+b29

(iii) (2p−3q)2=(2p)2−2×(2p)×(3q)+(3q)2=4p2−12pq+9q2

(iv) (x−2x)2=(x)2−2×(x)×(2x)+(2x)2=x2−4+4x2

(v) (ax+by)2=(ax)2+2×(ax)×(by)+(by)2=a2x2+2axby+b2y2

(vi) (7m−4)2=(7m)2−2×(7m)×(4)+(4)2=49m2−56m+16

(vii) (x+12)2=(x)2+2×(x)×(12)+(12)2=x2+x+14

(viii) (a−1a)2=(a)2−2×(a)×(1a)+(1a)2=a2−2+1a2