Question

(b) 50(2x + y)2 - 18(x – 2y)2​

Answer 1

Step-by-step explanation:

STEP1:Equation at the end of step 1

(50 • ((2x + y)2)) - 18 • (x - 2y)2

STEP2:Equation at the end of step 2

50 • (2x + y)2 - 18 • (x - 2y)2

STEP3:

3.1 Evaluate : (2x+y)2 = 4x2+4xy+y2

3.2 Evaluate : (x-2y)2 = x2-4xy+4y2

STEP4:Pulling out like terms

4.1 Pull out like factors :

182x2 + 272xy - 22y2 = 2 • (91x2 + 136xy - 11y2)

Trying to factor a multi variable polynomial :

4.2 Factoring 91x2 + 136xy - 11y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (13x - y)•(7x + 11y)

Final result :

2 • (13x - y) • (7x + 11y)

Answer 2

Step-by-step explanation:

50(2x+y)2-18(x-2y)2

=100(2x+y)-36(x-2y)

=200x+100y-36x+72y

=164x+172y

=4(41x+43y)