Advertisements
Advertisements
Question
Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z
Advertisements
Solution
The given expression is
`x^2 +y^2 +z^2 - xy +xz + yz`
We have to multiply the above expression by `(x+y-y)`.
The required product is
`(x+y-z)(x^2 + y^2 +z^2 -xy +xz +yz)`
`= {x+y + (-z)} {(x)^2 + (y^2) + (-z)^2 =- x,y-y (-z) - (-z).x}`
Recall the formula
`a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2+b^2+c^2 - ab - bc -ca)`
Using the above formula, we have
`=x^3 + y^3 + ( -z)^3 -3 .x.y.(-z)`
` = x^3 +y^3 - z^3 +3xyz`
APPEARS IN
RELATED QUESTIONS
Factorize the following expressions:
p3 + 27
Simplify `(155 xx 155 xx 155 - 55 xx 55 xx 55)/(155 xx 155 + 155 xx 55 + 55 xx 55)`
Factorize 8x3 + 27 y3 + 36x2 y + 54xy2
Find the value of x3 + y3 − 12xy + 64, when x + y =−4
Evaluate: `(1/2 "a" + 1/2 "b") (1/2 "a" - 1/2 "b")`
Divide: - 50 + 40p by 10p
Divide:
n2 − 2n + 1 by n − 1
Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
A student wrote an algebraic expression for “5 less than a number n divided by 3” as `n/3 - 5`. What error did the student make?
What type of algebraic expression is 2x−4y²?
