What must be subtracted from a^{3} – 4a^{2} + 5a – 6 to obtain a^{2} – 2a + 1?
Here, a^{3}– 4a^{2} + 5a – 6 – (a^{2} – 2a + 1)
= a^{3}– 4a^{2} + 5a – 6 – a^{2} + 2a – 1
= a^{3}– 5a^{2} + 7a – 7
By how much does 1 exceed 2x – 3y – 4 ?
Required difference = 1– (2x – 3y – 4)
= 3y – 2x + 5
How much less than l – 2m + 3n is 2l – 4m – n ?
Required difference
= (l – 2m + 3n) – (2l – 4m – n)
= – l + 2m + 4n
If x = – 2 y = – 1 and z = 3 then what is the value of x^{2} + y^{2} – z^{2}
Required value
= x^{2} + y^{2} – z^{2}
= (–2)^{2} + (–1)^{2}– (3)^{2} = 4 + 1 – 9
= 5 – 9 = – 4
What is the coefficient of m in –7 l2 mn ?
If x = 4, y = –1 and z = –2 then what is the value of 2x^{2} – y^{2} + 3z^{2} ?
2x^{2 }–y^{2} + 3z^{2}
= 2(4)^{2} – (–1)^{2} + 3(–2)^{2}
= 32 – 1 + 12 = 44 – 1= 43
What must be added to 5x^{3} – 2x^{2} + 6x + 7 to make the sum x^{3 }+ 3x^{2} – x + 1 ?
x^{3} + 3x^{2} – x + 1 – 5x^{3} + 2x^{2} – 6x – 7
= –4 x^{3} + 5x^{2} – 7x – 6
By how much is 2x – 3y + 4z greater than 2x + 5y – 6z + 2?
Required difference
= – (–2x – 5y + 6z – 2)
= – 8y + 10z – 2
What is the simplified value of 2x – [3y –{2x– (y – x)}]?
2x –[3y–{2x– (y–x)}]
= 2x –[3y–{2x– y + x)}]
= 2x –[3y–3x + y] = 2x – 4y + 3x = 5x–4y
What is the value of m if
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