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Algebraic Expressions and Identities

Short Answer Type

51.

Fint the product.

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52.

Fint the product.

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53.

Find the product.

X x X²x X³x X⁴

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54.

Simplify 3x(4x - 5) + 3 and find its values for (i) x = 3 (ii) $space space space space space space space space straight x space equals space 1 half$

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55.

simplify a(a²+ a + 1) + 5 and find its values for (i) a = 0, (ii) a = 0, and (iii) a = -1.

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56.

(a) Add: p(p – q), q(q – r) and r(r – p)

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57.

Add: 2x(z – x – y) and 2y(z – y – x)

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58.

Subtract: 3l(l – 4m + 5n) from 41(10n + 3m + 2l)

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59.
Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(–a + b + c)

∵ 3a(a + b + c) – 2b(a – b + c)

                     = (3a x a + 3a x b + 3a x c) -(2b x a + 2b x (-b) + 2b x c)
                     = (3a²+ 3ab + 3ac) - (2ab - 2b²+ 2bc)
                     = 3a²+ 3ab + 3ac- 2ab - 2b²+ 2bc
                     = 3a²+ ab + 3ac + 2b² - - 2ab

and 4c(-a + b + c) = 4c x (-a) + 4c x b +4c x c
                          = -4ac + 4bc + 4c²

∴    -4ac + 4bc + 4c²
        3ac   - 2bc + 3a² + ab + 2b²
        (-)      (+)     (-)   (-)   (-)
_______________________________________
(-4 - 3)ac + ( 4 + 2)bc + 4c² -3a²-ab -2b²

= -7ac + 6bc + 4c²-3a²
= -3a²--2b²+4c²-ab+6 bc - 7ac

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