1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The value of ∣∣ ∣∣3x−x+y−x+zx−y3yz−yx−zy−z3z∣∣ ∣∣ equals to

A
6(x+y+z)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3(x+y+z)(xy+yz+zx)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
6(x+y+z)(xy+yz+zx)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
9(x+y)(xy+2yz)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 3(x+y+z)(xy+yz+zx)We have ∣∣ ∣∣3x−x+y−x+zx−y3yz−yx−zy−z3z∣∣ ∣∣ Applying C1→C1+C2+C3 =∣∣ ∣∣x+y+z−x+y−x+zx+y+z3yz−yx+y+zy−z3z∣∣ ∣∣ Taking (x+y+z) common from C1 =(x+y+z)∣∣ ∣∣1−x+y−x+z13yz−y1y−z3z∣∣ ∣∣ Applying R2→R2−R1 and R3→R3−R1 =(x+y+z)∣∣ ∣∣1−x+y−x+z02y+xx−y0x−z2z+x∣∣ ∣∣ Applying C2→C2−C3 =(x+y+z)∣∣ ∣∣1y−z−x+z03yx−y0−3z2z+x∣∣ ∣∣ Expanding along first column, we get (x+y+z)⋅1[3y(2z+x)+(3z)(x−y)]=(x+y+z)(3yz+3yx+3xz)=3(x+y+z)(xy+yz+zx)

Suggest Corrections
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program