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प्रश्न
Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z
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उत्तर
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`
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| x4 | |||||
| (___) | 4x5y4 | ||||
| −x2y | |||||
| 2y2z | −10xy2z3 | ||||
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| Column I | Column II |
| 1. The difference of 3 and a number squared | (a) 4 – 2x |
| 2. 5 less than twice a number squared | (b) n2 – 3 |
| 3. Five minus twice the square of a number | (c) 2n2 – 5 |
| 4. Four minus a number multiplied by 2 | (d) 5 – 2n2 |
| 5. Seven times the sum of a number and 1 | (e) 3 – n2 |
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| 7. 2 times the sum of a number and 6 | (g) 7(n + 1) |
| 8. Three less than the square of a number | (h) n2 + 6 |
