Subtract the sum of 3-2-2-5 and -2-5-7 from the sum of5-2-9-3 and 2-2-1-

Step 1 : Find the sum of (3𝑎^2−2𝑎+5 ) and (𝑎^2−5𝑎−7 ) Sum of (3𝑎^2−2𝑎+5 ) and (𝑎^2−5𝑎−7 ) = (3𝑎^2−2𝑎+5 )+ (𝑎^2−5𝑎−7 ) = 3𝑎^2+𝑎^2−2𝑎−5𝑎+5−7 = 4𝑎^2−7𝑎−2 ….(1) Ste ...

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Standard X

Mathematics

Quadratic Formula

Subtract the ...

Question

Subtract the sum of $3 a^{2} - 2 a + 5$ and $a^{2} - 5 a - 7$ from the sum of $5 a^{2} - 9 a + 3$ and $2 a - a^{2} - 1.$

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Solution

Step 1 : Find the sum of $(3 a^{2} - 2 a + 5)$ and $(a^{2} - 5 a - 7)$ Sum of $(3 a^{2} - 2 a + 5)$ and $(a^{2} - 5 a - 7)$ $= (3 a^{2} - 2 a + 5) + (a^{2} - 5 a - 7)$ $= 3 a^{2} + a^{2} - 2 a - 5 a + 5 - 7$
$= 4 a^{2} - 7 a - 2$ ….(1)
Step 2 : Find the sum of $(5 a^{2} - 9 a + 3)$ and $(2 a - a^{2} - 1)$ Sum of $(5 a^{2} - 9 a + 3)$ and $(2 a - a^{2} - 1)$ $= 5 a^{2} - 9 a + 3 + 2 a - a^{2} - 1$ $= 5 a^{2} - a^{2} - 9 a + 2 a + 3 - 1$
$= 4 a^{2} - 7 a + 2$ …..(2)
Step 3: Find the required diffrence $(4 a^{2} - 7 a + 2) - (4 a^{2} - 7 a - 2)$ $= 4 a^{2} - 7 a + 2 - 4 a^{2} + 7 a + 2$ $= 4 a^{2} - 4 a^{2} - 7 a + 7 a + 2 + 2$
= 4
Hence, the required difference is 4.

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Subtract the sum of 3a2−2a+5 and a2−5a−7 from the sum of5a2−9a+3 and 2a−a2−1.

Subtract the sum of $3 a^{2} - 2 a + 5$ and $a^{2} - 5 a - 7$ from the sum of $5 a^{2} - 9 a + 3$ and $2 a - a^{2} - 1.$