Question

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Answer 1

(i) $(3p+2q)(9p^{2} -6pq+4q^{2} )$

Answer

$(3p+2q)(9p^{2} -6pq+4q^{2} )$

$(3p+2q)(9p^{2} +-6pq+4q^{2} )$

$(3p)(9p^{2})+(3p)(-6pq) +(3p)(4q^{2} )+(2q)(9p^{2} )+(2q)(-6pq)+(2q)(4q^{2} )$

$27p^{3} -18p^{2} q+12pq^{2} +18p^{2} q-12pq^{2} +8p^{3}$

$27p^{3}+8q^{3}$

(ii) $(4a-5b)(16a^{2}+20ab+25b^{2} )$

Answer

$(4a-5b)(16a^{2}+20ab+25b^{2} )$

$(4a+-5b)(16a^{2} +20ab+25b^{2} )$

$(4a)(16a^{2} )+(4a)(20ab)+(4a)(25b^{2})+(-5b)(16a^{2})+(-5b)(20ab)+ (-5b)(25b^{2} )$

$64a^{3}+80a^{2}b+100ab^{2} -80a^{2}b-100ab^{2} -125b^{3}$

$64a^{3}-125b^{3}$

(iii) $(7x+y)(49x^{2} -7xy+y^{2} )$

Answer

$(7x+y)(49x^{2} -7xy+y^{2} )$

$(7x+y)(49x^{2} +-7xy+y^{2} )$

$(7x)(49x^{2} )+(7x)(-7xy)+(7x)(y^{2} )+(y)(49x^{2} )+(y)(-7xy)+(y)(y^{2} )$

$343x^{3} -49x^{2} y+7xy^{2} +49x^{2} y-7xy^{2} +y^{3}$

$343x^{3} +y^{3}$

(iv) $(3x^{4}+5)(9x^{8}-15x^{4}+25)$

Answer

$(3x^{4}+5)(9x^{8}-15x^{4}+25)$

$(3x^{4}+5)(9x^{8}+-15x^{4}+25)$

$(3x^{4} )(9x^{8} )+(3x^{4} )(-15x^{4} )+(3x^{4} )(25)+(5)(9x^{8} )+(5)(-15x^{4} )+(5)(25)$

$27x^{12} -45x^{8} +75x^{4} +45x^{8} -75x^{4} +125$

$27x^{12} +125$

Answer 2

Answer:

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(i) (3p+2q)(9p^{2} -6pq+4q^{2} )(3p+2q)(9p2−6pq+4q2)

Answer

(3p+2q)(9p^{2} -6pq+4q^{2} )(3p+2q)(9p2−6pq+4q2)

(3p+2q)(9p^{2} +-6pq+4q^{2} )(3p+2q)(9p2+−6pq+4q2)

(3p)(9p^{2})+(3p)(-6pq) +(3p)(4q^{2} )+(2q)(9p^{2} )+(2q)(-6pq)+(2q)(4q^{2} )(3p)(9p2)+(3p)(−6pq)+(3p)(4q2)+(2q)(9p2)+(2q)(−6pq)+(2q)(4q2)

27p^{3} -18p^{2} q+12pq^{2} +18p^{2} q-12pq^{2} +8p^{3}27p3−18p2q+12pq2+18p2q−12pq2+8p3

27p^{3}+8q^{3}27p3+8q3

(ii) (4a-5b)(16a^{2}+20ab+25b^{2} )(4a−5b)(16a2+20ab+25b2)

Answer

(4a-5b)(16a^{2}+20ab+25b^{2} )(4a−5b)(16a2+20ab+25b2)

(4a+-5b)(16a^{2} +20ab+25b^{2} )(4a+−5b)(16a2+20ab+25b2)

(4a)(16a^{2} )+(4a)(20ab)+(4a)(25b^{2})+(-5b)(16a^{2})+(-5b)(20ab)+ (-5b)(25b^{2} )(4a)(16a2)+(4a)(20ab)+(4a)(25b2)+(−5b)(16a2)+(−5b)(20ab)+(−5b)(25b2)

64a^{3}+80a^{2}b+100ab^{2} -80a^{2}b-100ab^{2} -125b^{3}64a3+80a2b+100ab2−80a2b−100ab2−125b3

64a^{3}-125b^{3}64a3−125b3

(iii) (7x+y)(49x^{2} -7xy+y^{2} )(7x+y)(49x2−7xy+y2)

Answer

(7x+y)(49x^{2} -7xy+y^{2} )(7x+y)(49x2−7xy+y2)

(7x+y)(49x^{2} +-7xy+y^{2} )(7x+y)(49x2+−7xy+y2)

(7x)(49x^{2} )+(7x)(-7xy)+(7x)(y^{2} )+(y)(49x^{2} )+(y)(-7xy)+(y)(y^{2} )(7x)(49x2)+(7x)(−7xy)+(7x)(y2)+(y)(49x2)+(y)(−7xy)+(y)(y2)

343x^{3} -49x^{2} y+7xy^{2} +49x^{2} y-7xy^{2} +y^{3}343x3−49x2y+7xy2+49x2y−7xy2+y3

343x^{3} +y^{3}343x3+y3

(iv) (3x^{4}+5)(9x^{8}-15x^{4}+25)(3x4+5)(9x8−15x4+25)

Answer

(3x^{4}+5)(9x^{8}-15x^{4}+25)(3x4+5)(9x8−15x4+25)

(3x^{4}+5)(9x^{8}+-15x^{4}+25)(3x4+5)(9x8+−15x4+25)

(3x^{4} )(9x^{8} )+(3x^{4} )(-15x^{4} )+(3x^{4} )(25)+(5)(9x^{8} )+(5)(-15x^{4} )+(5)(25)(3x4)(9x