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Add the following: a – b + ab, b – c + b...

Add the following: a – b + ab, b – c + bc, c – a + ac

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If a, b,c are in G.P., prove that the following are also in G.P. : a^(2)+b^(2),ab+bc,b^(2)+c^(2) .

Write the value of the following determinant abs{:(a-b, b-c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c):} .

Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,ca,ab)|=(a-b)(b-c)(c-a)(ab+bc+ca)

If (lna)/(b-c)=(lnb)/(c-a)=(lnc)/(a-b) , prove the following . a^(b^2+bc+c^2).b^(c^2+ca+a^2).c^(a^2+ab+b^2)=1

Compute the following: : [[a^2+b^2,b^2+c^2],[a^2+c^2,a^2+b^2]] + [[2ab,2bc],[-2ac,-2ab]]

Without expanding, prove the following |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(a+b+c)(ab+bc+ca-a^2-b^2-c^2)

PSEB-ALGEBRAIC EXPRESSIONS AND IDENTITIES-EXERCISE
  1. Classify the following polynomials as monomials, binomials, trinomials...

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  2. Add the following: ab – bc, bc – ca, ca – ab

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  3. Add the following: a – b + ab, b – c + bc, c – a + ac

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  4. Add the following: 2p^2q^2 – 3pq + 4, 5 + 7pq – 3p^2q^2

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  5. Add the following: l^2 + m^2, m^2 + n^2, n^2 + l^2, 2lm + 2mn + 2nl

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  6. Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3

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  7. Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

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  8. Subtract 4p^2q – 3pq + 5pq^2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq –...

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  9. Find the product of the following pairs of monomials: 4, 7p

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  10. Find the product of the following pairs of monomials: – 4p, 7p

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  11. Find the product of the following pairs of monomials: – 4p, 7pq

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  12. Find the product of the following pairs of monomials: 4p^3, – 3p

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  13. Find the product of the following pairs of monomials: 4p, 0

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  14. Find the areas of rectangles with the following pairs of monomials as ...

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  15. Obtain the volume of rectangular boxes with the following length, brea...

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  16. Obtain the volume of rectangular boxes with the following length, brea...

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  17. Obtain the volume of rectangular boxes with the following length, brea...

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  18. Obtain the volume of rectangular boxes with the following length, brea...

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  19. Obtain the product of : xy, yz, zx

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  20. Obtain the product of : a, – a^2, a^3

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