प्रश्नावली-4E
1. गुणनफल ज्ञात कीजिए-
(i)5a×9b
(ii)15a2×4a3
(iii)0.8a×0.7b
(iv)0.72a2b×0.3ab2
(v)3a2b4×5a3b6
उत्तर:—
(i)5a×9b
=45ab
(ii)15a2×4a3
=15×4×a2×a3
=60a5
(iii)0.8a×0.7b
=0.8×0.7×a×b
=0.56ab
(iv)0.72a2b×0.3ab2
=0.72×0.3×a2b×ab2
=0.216a3b3
(v)3a2b4×4a3b6
=3×4×a2b4×a3b6
=12a5b10
2.(i)3a(4a+9c)
(ii)2a2(4a3+9a5)
उत्तर:—
(i)3a(4b+9c)
=3a×4b+3a×9c
=12ab+27ac
(ii)2a2(4a3+9a5)
=2a2×4a3+2a2×9a5
=8a5+18a7
3.(i) (3x-5) (4x+7)
(ii)(2a+3b)(4a+6b)
(iii) (4pq-6r)(pq-2s)
उत्तर:—
(i)(3x-5)(4x+7)
=3x×4x+3x×7-5×4x-5×7
=12×2+21x-20x-35
=12×2+x-35
(ii)(2a+3b)(4a+6b)
=2a×4a+2a×6b+3b×4a+3b×6b
=8a2+12ab+12ab+18b2
=8a2+24ab+18b2
(iii)(4pq-6r) (pq-2s)
=4pq×pq+4pq×(-2s)-6r×pq-6r×(-2)
=4p2q2-8pqs-6pqr+12rs
4. सरल करें—
(i)(x-y)(x2+xy)+(x-y)y2
(ii)(4x-2y)(3x+2y)-(2x+3y)(5x-2y)
उत्तर:—
(i)(x-y)(x2+xy)+(x-y)y2
=x×x2+x×xy-y×x2-y×xy+x×y2-y×y2
=x3+x2y-x2y-xy2+xy2-y3
=x3-y3
(ii)(4x-2y)(3x+2y)-(2x+3y)(5x-2y)
=4x×3x+4x×2y-2y×3x-2y×2y-{(2x×5x+2x×(-2y)+3y×5x+3y×(-2y)}
=12×2+8xy-6xy-4y2-(10×2-4xy+15xy-6y2)
=12×2+8xy-6xy-4y2-10×2+4xy-15xy+6y2
=12×2+2xy+2y2-10×2-11xy
=2×2+2y2-9xy
=2×2-axy+2y2
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