The factored form of the expression 4ry + 3rz + 8xy + 6xz is given by: Option D: (4y + 3z)(2x + r)
What is the factored form of an expression?
When an expression is written as result of multiplication of some terms, then that multiplication form is called the factored form of that expression.
Example: \(6 = 3\times 2\) is a factored way of writing 6.
We've to find the factored form of 4ry + 3rz + 8xy + 6xz
Since twice of 4 is 8, and twice of 3 is 6, so that might help:
\(4ry + 3rz + 8xy + 6xz = 4ry + 8xy+ 3rz + 6xz\\4ry + 3rz + 8xy + 6xz = 4y(r+2x) + 3z(r+2x)\\4ry + 3rz + 8xy + 6xz = (r+2x)(4y+3z)\\4ry + 3rz + 8xy + 6xz = (4y+3z)(2x+r)\)
The last step was just to make it match with some of the option available(to which it matches in value) without distorting the value of the expression.
Thus, the factored form of the expression 4ry + 3rz + 8xy + 6xz is given by: Option D: (4y + 3z)(2x + r)
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