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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)

∵ p(p - q) = p x p - p x q = p²- pq
q(q - r) = q x q - q x r = q²- qr
and r ( r - p) = r x r -r x p = r²- rp

∴ adding the above products, we have

(p²- pq ) + (q²- qr) + (r²- rp) = p²- pq + q²- qr + r²- rp
= p²+ q²+ r²- pq - qr - rp
= p²+ q²+ r²- (pq + qr + rp)