Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
$(i)$ Subtraction of $z$ from $y$.
$(ii)$ One-half of the sum of numbers x and y.
$(iii)$ The number z multiplied by itself.
$(iv)$ One-fourth of the product of numbers p and q.
$(v)$ Numbers x and y both squared and added.
$(vi)$ Number 5 added to three times the product of numbers m and n.
$(viii)$ Product of numbers y and z subtracted from 10.
$(viii)$ Sum of numbers a and b subtracted from their product.

To do: To get the algebraic expressions in the given cases using variables, constants, and arithmetic operations.

Solution:

$(i)$: Subtraction of $z$ from $y$.

$y-z$

$(ii)$: One-half of the sum of numbers $x$ and $y$.

$\frac{1}{2}(x+y)$ or $\frac{x+y}{2}$

$(iii)$: The number $z$ multiplied by itself.

$z\times z=z^2$

$(iv)$: One-fourth of the product of numbers $p$ and $q$.

$\frac{1}{4}pq$ or $\frac{pq}{4}$

$(v)$: Numbers $x$ and $y$ are both squared and added.

${x^2+y^2}$

$(vi)$: Number $5$ added to three times the product of numbers $m$ and $n$.

$3mn+5$

$(viii)$: Product of numbers $y$ and $z$ subtracted from $10$.

$10-yz$

$(viii)$: Sum of numbers a and b subtracted from their product.

$ab-(a+b)$

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Updated on: 10-Oct-2022

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