1
Question
Solve:4yz(z2+6z−16)÷2y(z+8)
Solve:4yz(z2+6z−16)÷2y(z+8)
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Solution
The correct option is D 2z(z−2)
Given, the expression is
4yz(z2+6z−16)2y(z+8).
First, we will factorise (z2+6z−16).
Comparing the above expression with the identity x2+(a+b)x+ab, we note that, (a+b)=6 and ab=−16.
Since,
8+(−2)=6 and (8)(−2)=−16,
the expression, z2+6z−16
=z2+8z−2z−16
=z(z+8)−2(z+8)
=(z−2)(z+8) . . . (i)
By substituting (i) in the given expression, we get
=4yz(z−2)(z+8)2y(z+8)
=4×y×z×(z−2)×(z+8)2×y×(z+8)
=2z(z−2)
2z(z−2)
Given, the expression is
4yz(z2+6z−16)2y(z+8).
First, we will factorise (z2+6z−16).
Comparing the above expression with the identity x2+(a+b)x+ab, we note that, (a+b)=6 and ab=−16.
Since,
8+(−2)=6 and (8)(−2)=−16,
the expression, z2+6z−16
=z2+8z−2z−16
=z(z+8)−2(z+8)
=(z−2)(z+8) . . . (i)
By substituting (i) in the given expression, we get
=4yz(z−2)(z+8)2y(z+8)
=4×y×z×(z−2)×(z+8)2×y×(z+8)
=2z(z−2)
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