find the product of (X - 2)(3 - 2x)(3 x - 7)
Answers
Step-by-step explanation:
Question
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Find each of the following products:
(x
2
−3x+7)×(2x+3)
Medium
Solution
verified
Given (x
3
−3x+7)×(2x+3)
To find the product of given expression we have to use horizontal method.
In that we have to multiply each term of one expression with each term of another
Expression so by multiplying we get,
(x
3
−3x+7)×(2x+3)
⇒2x(x
2
−3x+7)+3(x
2
−3x+7)
⇒2x
3
−6x
2
+14x+3x
2
−9x+21
⇒2x
3
−3x
2
+5x+21
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Q2) Find the product:
(i) (5 - 2x)(3 + x)
(ii) (x + 7y)(7x - y)
(iii) \left(a^2+b\right)\left(a+b^2\right)(a
2
+b)(a+b
2
)
(iv) \left(p^2-q^2\right)\left(2p+q\right)(p
2
−q
2
)(2p+q)
Solution:
(i) \left(5-2x\right)\left(3+x\right)(5−2x)(3+x)
= 5\times\left(3+x\right)-2x\left(3+x\right)\5×(3+x)−2x(3+x)
= 5\times3+5\times x-2x\times3-2x\times x5×3+5×x−2x×3−2x×x
= 15+5x-6x-2x^215+5x−6x−2x
2
= 15-x-2x^215−x−2x
2
(ii) \left(x+7y\right)\left(7x-y\right)(x+7y)(7x−y)
= x\left(7x-y\right)+7y\times\left(7x-y\right)x(7x−y)+7y×(7x−y)
= x\times7x-x\times y+7y\times7x-7y\times yx×7x−x×y+7y×7x−7y×y
= 7x^2-xy+49xy-7y^27x
2
−xy+49xy−7y
2
= 7x^2+48xy-7y^27x
2
+48xy−7y
2
(iii) \left(a^2+b\right)\left(a+b^2\right)(a
2
+b)(a+b
2
)
= a^2\times\left(a+b^2\right)+b\times\left(a+b^2\right)a
2
×(a+b
2
)+b×(a+b
2
)
= a^2\times a+a^2\times b^2+b\times a+b\times b^2a
2
×a+a
2
×b
2
+b×a+b×b
2
= a^3+a^2b^2+ab+b^3a
3
+a
2
b
2
+ab+b
3
(iv) \left(p^2-q^2\right)\left(2p+q\right)(p
2
−q
2
)(2p+q)
= p^2\times\left(2p+q\right)-q^2\left(2p+q\right)p
2
×(2p+q)−q
2
(2p+q)
= p^2\times2p+p^2\times q-q^2\times qp
2
×2p+p
2
×q−q
2
×q
= 2p^3+p^2q-2pq^2-q^32p
3
+p
2
q−2pq
2
−q
3